The largest number of weights in cyclic codes

07/23/2018

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by   Minjia Shi, et al.

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Upper and lower bounds on the largest number of weights in a cyclic code of given length, dimension and alphabet are given. An application to irreducible cyclic codes is considered. Sharper upper bounds are given for cyclic codes (called here strongly cyclic), all codewords of which have period the length. Asymptotics are derived on the function Γ(k,q), the largest number of nonzero weights a cyclic code of dimension k over _q can have, and an algorithm to compute it is sketched.