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Article Dans Une Revue IEEE Transactions on Information Theory Année : 2017

Two New Families of Two-Weight Codes

Résumé

We construct two new infinite families of trace codes of dimension $2m$, over the ring $\mathbb{F}_p+u\mathbb{F}_p,$ when $p$ is an odd prime. They have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using Gauss sums. By Gray mapping, we obtain two infinite families of linear $p$-ary codes of respective lengths $(p^m-1)^2$ and $2(p^m-1)^2.$ When $m$ is singly-even, the first family gives five-weight codes. When $m$ is odd, and $p\equiv 3 \pmod{4},$ the first family yields $p$-ary two-weight codes, which are shown to be optimal by application of the Griesmer bound. The second family consists of two-weight codes that are shown to be optimal, by the Griesmer bound, whenever $p=3$ and $m \ge 3,$ or $p\ge 5$ and $m\ge 4.$ Applications to secret sharing schemes are given.
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Dates et versions

hal-04089086 , version 1 (04-05-2023)

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Minjia Shi, Yue Guan, Patrick Sole. Two New Families of Two-Weight Codes. IEEE Transactions on Information Theory, 2017, 63 (10), pp.6240-6246. ⟨10.1109/TIT.2017.2742499⟩. ⟨hal-04089086⟩
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