I have told about Intersection Array before, now I will post a program to compute it.
This program has been developed by CCG group, directed by Jaume Pujol and programed by me.
There are various options to use the program:
The program is under GPLv3 license and you can download it from CCGroup
The zip is composed by the source code, the documentation (with some exemples) and a binary.
All you can expect to know is explained on the documentation, in fact, I will sum up the uses of the program.
You can use it to compute the intersection array of a given vector in a code. It will show only the column corresponding to the distance of the vector.
You can also try all the posible distance if you know the covering radius of the code. Then the program will search a vector for each distance lesser than covering radius, and it will compute the intersection array.
You can use it to know if a code is completly regular. When this option is set, you must specify a hamming weight, then it will try all the posible vectors of the same weight and check if they have the same intersection array, until the specified weight or until the word length (there can't exist a vector with hamming weiht > word length). This is an important option, because the problem of knowing if a code is completly regular is a non-polynomial problem. This is, a completly regular code is a code which all the vectors at the same distance to the code, have the same intersection array.
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Hi Bernat I would Like to asck you what avantages have using Intersection arrays in oder to compute if a code is completly regular upon other methods like using a characterization of completely regular codes through p-polynomial association schemes.
That's an interesting question. The problem we have computing CR codes is a hardware limit. When we have a big code, we will have problems to check if this code is a CRC because of the complexity. But, if a code is not a CRC it usually fails when testing few vectors. So the real problem comes with those big CRC. When checking them via Intersection Array we can set a number of iterations, and we can be nearly sure that if it do not fail in a big amount of iterations, this code is a CRC. This is the principal adventage.
I am documenting an aplication we used to use to compute crc, it's really optimum, but it has the problem of checking big CRC. That's why we thought about IA to check CRC. I will post it soon.
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