#### Topic: QR-code

It is not assured that it here was, and is not assured that it for programmers. But to backs. We imagine that we develop the standard of a QR-code. Our QR-code of the size NxN is a small square from N x N pixels. Each pixel black or white. Difficulty consists that when we scan the code, we do not know, what side turns a square. 4 variants (0, 90, 180 and 270 degrees) the Question are possible all: how many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation.

#### Re: QR-code

Hello, Erop, you wrote: E> the Question? How many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation. That did not depend, or that it was possible to recognize orientation and to recover the encoded?

#### Re: QR-code

Hello, Erop, you wrote: E> it is not assured that it here was, and is not assured that it for programmers. E> but to backs. E> we develop the standard of a QR-code. E> our QR-code of the size NxN is a small square from N x N pixels. Each pixel black or white. E> difficulty consists that when we scan the code, we do not know, what side turns a square. 4 variants (0, 90, 180 and 270 degrees) E> the Question are possible all? How many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation. Not  will be, if the square consists of identical quarters whereas do not turn - it will be identical to look.

#### Re: QR-code

Hello, Erop, you wrote: E> it is not assured that it here was, and is not assured that it for programmers. E> but to backs. E> we develop the standard of a QR-code. E> our QR-code of the size NxN is a small square from N x N pixels. Each pixel black or white. E> difficulty consists that when we scan the code, we do not know, what side turns a square. 4 variants (0, 90, 180 and 270 degrees) E> the Question are possible all? How many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation. In other words, all your images should possess an axis of symmetry of 4th order? In that case number of variants for even N: - 2 ^ (N^2/4), for odd: 2 ^ ((N-1) ^2/4 + (N-1)/2 + 1).

#### Re: QR-code

Hello, Erop, you wrote: E> Our QR-code of the size NxN is a small square from N x N pixels. Each pixel black or white. E> difficulty consists that when we scan the code, we do not know, what side turns a square. 4 variants (0, 90, 180 and 270 degrees) E> the Question are possible all? How many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation. We color, for example, two upper corners in black color, lower left - in white. It suffices for orientation determination. Remains 2 ^ (N^2-3) variants.

#### Re: QR-code

Hello, Brice Tribbiani, you wrote: BT> we Color, for example, two upper corners in black color, lower left - in white. It suffices for orientation determination. BT> Remains 2 ^ (N^2-3) variants. For N = 2 it is explicitly suboptimal (two variants against really possible six), for N = 1 generally the hogwash turns out

#### Re: QR-code

Hello, Brice Tribbiani, you wrote: E>> the Question? How many different unique numbers it is possible to encode such code so, what the read out number did not depend on square orientation. BT> we color, for example, two upper corners in black color, lower left - in white. It suffices for orientation determination. BT> Remains 2 ^ (N^2-3) variants. As I understood, the task of recognition of orientation is not put at all. "Did not depend on square orientation" means that the image should not change from picture turn on 90 degrees. Is not present unless?

#### Re: QR-code

Hello, Pzz, you wrote: Pzz> That did not depend, or that it was possible to recognize orientation and to recover the encoded? It is necessary to be able to distinguish one number from another, to recover orientation it is not necessary

#### Re: QR-code

Hello, Qulac, you wrote: Q> Not  will be, if the square consists of identical quarters whereas do not turn - it will be identical to look. Well, it is obvious that it is possible to encode more numbers...

#### Re: QR-code

Hello, Erop, you wrote: E> Hello, Qulac, you wrote: Q>> Not  will be, if the square consists of identical quarters whereas do not turn - it will be identical to look. E> well, it is obvious that it is possible to encode more numbers... How?

#### Re: QR-code

Hello, rg45, you wrote: R> In other words, all your images should possess an axis of symmetry of 4th order? In that case number of variants for even N: - 2 ^ (N^2/4), for odd: 2 ^ ((N-1) ^2/4 + (N-1)/2 + 1). 1) At all is not present. It is possible to use more artful codings. Well, say, it is possible to color always three salient points in white, and one in black, and a square to turn so, what a black corner on the right-above. Remaining pixels to renumber and we receive 2 ^ (N*N-4) numbers that for N = 10 it is strong more than your estimation... 2) Why on "you"? There and then on "you" it is accepted? p.s. It is possible, for example, to try to invent the coding for N == 2. How many the different codes steady against turn it is possible to offer? We tell your formula for N == 2 gives 2 different numbers. It is obvious, what the coding "number of black pixels" gives 5 different numbers, and it is even more possible?

#### Re: QR-code

Hello, Brice Tribbiani, you wrote: BT> we Color, for example, two upper corners in black color, lower left - in white. It suffices for orientation determination. BT> Remains 2 ^ (N^2-3) variants. For example for N=2 it is 2 numbers. The coding "number of black pixels" gives 5 numbers... And it is even more possible?

#### Re: QR-code

Hello, Qulac, you wrote: Q> As? Well in it the question also consists it is necessary 1) to Specify a method More truly to reach a maximum 2) to Show that cannot be more

#### Re: QR-code

Hello, Erop, you wrote: E> We develop the standard of a QR-code. R>> in other words, all your images should possess an axis of symmetry of 4th order? In that case number of variants for even N: - 2 ^ (N^2/4), for odd: 2 ^ ((N-1) ^2/4 + (N-1)/2 + 1). E> 2) Why on "you"? There and then on "you" it is accepted? And I unless from capital letter wrote "yours"? You develop the standard of the code, therefore and pictures too yours

#### Re: QR-code

Hello, rg45, you wrote: R> As I understood, the task of recognition of orientation is not put at all. "Did not depend on square orientation" means that the image should not change from picture turn on 90 degrees. Is not present unless? No, roughly speaking, it is necessary to write the program to which you give numbers m> 0 and N> 0 and it prints square NxN or says that m is too great Also the second to which you give square NxN turned on an unknown corner (from 0, 90, 180, 270), and it prints m thus it is necessary that the program would reject as it is possible big m. Well also ask not the program, and dependence maximum possible m from N

#### Re: QR-code

Hello, Erop, you wrote: R>> In other words, all your images should possess an axis of symmetry of 4th order? E> 1) at all is not present. It is possible to use more artful codings. E> well, say, it is possible to color always three salient points in white, and one in black, and a square to turn so, what a black corner on the right-above. Remaining pixels to renumber and we receive 2 ^ (N*N-4) numbers that for N = 10 it is strong more than your estimation... Means, I simply truly treated expression "depended on square orientation". I would reformulate a question in that case: "how to provide recognition of orientation with a minimum overhead charge and what the useful capacity thus will be?". Correctly?

#### Re: QR-code

Hello, Erop, you wrote: R>> for the odd: 2 ^ ((N-1) ^2/4 + (N-1)/2 + 1). By the way, and why such artful formula? It would Seem, number of "unique" pixels in "" (N*N-1) / 4 well and one central is not forgotten. Also we receive 2 ^ ((N*N-1)/4 + 1) If to enter exact divisions (for example as//) it it is possible and so: 2 ^ (N*N//4 + 1) or 2 ^ ((N*N+3)//4) which is true for any N

#### Re: QR-code

Hello, Erop, you wrote: E> Hello, rg45, you wrote: R>> As I understood, the task of recognition of orientation is not put at all." Did not depend on square orientation "means that the image should not change from picture turn on 90 degrees. Is not present unless? E> Is not present, roughly speaking, it is necessary to write the program to which you give numbers m> 0 and N> 0 and it prints square NxN or says that m is too great E> And the second to which you give square NxN turned on an unknown corner (from 0, 90, 180, 270), and it prints m E> thus it is necessary that the program would reject as it is possible big m. E> Well also ask not the program, and dependence maximum possible m from N a square there is no selected orientation, . it is symmetric. Means the square is necessary not. For example: one pixel in left upper to a corner is done black, pixels round it always white and are not used for record, is similar on remaining corners white not used fields 2 on . Because of black pixel of symmetry is not present and it is possible to recognize orientation. P.S. Optimal it to use not a square, and for example a square-topped triangle. Generally, it is necessary to note, the problem of search of a qr-code not where does not disappear. Suddenly almost all pixels will be white how then to recognize qr-code boundaries? Without special labels here as and if there are labels it is possible to learn and orientation.

#### Re: QR-code

Hello, Erop, you wrote: E> For example for N=2 it is 2 numbers. E> the coding "the number of black pixels" gives 4 numbers... 5

#### Re: QR-code

Hello, rg45, you wrote: R> Means, I simply truly treated expression "depended on square orientation". I would reformulate a question in that case: "how to provide recognition of orientation with a minimum overhead charge and what the useful capacity thus will be?". Correctly? Yes, only to define orientation it is not necessary

#### Re: QR-code

Hello, Erop, you wrote: R>>> for the odd: 2 ^ ((N-1) ^2/4 + (N-1)/2 + 1). E> By the way, and why such artful formula? It would Seem, number of "unique" pixels in "" (N*N-1) / 4 well and one central is not forgotten. Also we receive 2 ^ ((N*N-1)/4 + 1) Well so simplify my expression, the same and turns out. I wrote how to me to represent was easier.

#### Re: QR-code

Hello, Brice Tribbiani, you wrote: E>> the coding "the number of black pixels" gives 4 numbers... BT> 5 Yes! Was mistaken And it is possible more?

#### Re: QR-code

Hello, rg45, you wrote: E>> By the way, and why such artful formula? It would Seem, number of "unique" pixels in "" (N*N-1) / 4 well and one central is not forgotten. Also we receive 2 ^ ((N*N-1)/4 + 1) R> Well so simplify my expression, the same and turns out. I wrote how to me to represent was easier. Well here and interesting that it was easier to you to represent. I wrote, how the formula was deduced by me?

#### Re: QR-code

Hello, Erop, you wrote: R>> Well so simplify my expression, the same and turns out. I wrote how to me to represent was easier. E> well here and interesting that it was easier to you to represent. I wrote, how the formula was deduced by me? I counted separately slices of central columns and separately square matrixes, well and  , here that triple of items and turned out.

#### Re: QR-code

Hello, Erop, you wrote: E> And it is possible more? For two 6 maximum. 1. One corner black (3 more turn out its rotation) 2. One side black (3 more turn out rotation) 3. One diagonal black (one more turns out its rotation) 4. One corner white (3 more turn out its rotation) 5. All black. 6. All white.