Optimal Ternary Cubic Two‐Weight Codes. Issue 4 (1st July 2018) - Shi, Minjia; Huang, Daitao; Solé, Patrick
Abstract : We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi‐cyclic of coindex three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly‐even. When mis odd, under some hypothesises on the size of L, we obtain two new infinite families of two‐weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.