Binary cyclic codes generated by m1m7
IEEE Transactions on Information Theory
On the minimum distance of cyclic codes
IEEE Transactions on Information Theory
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Hyperplane Sections of Fermat Varieties in P3 in Char.2 and Some Applications to Cyclic Codes
AAECC-10 Proceedings of the 10th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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We consider the weight distribution of the binary cyclic code of length 2^n-1 with two zeros @a^a,@a^b. Our proof gives information in terms of the zeta function of an associated variety. We carry out an explicit determination of the weight distribution in two cases, for the cyclic codes with zeros @a^3,@a^5 and @a,@a^1^1. These are the smallest cases of two infinite families where finding the weight distribution is an open problem. Finally, an interesting application of our methods is that we can prove that these two codes have the same weight distribution for all odd n.