Two-weight codes from trace codes over $R_k$
Minjia Shi, Yue Guan
TL;DR
This paper constructs two-Lee-weight codes over a ring using trace codes with abelian structure, determines their weight distribution, and derives optimal binary codes with applications to secret sharing.
Contribution
It introduces a new family of two-weight codes over rings with explicit weight distribution and demonstrates their optimality and application in secret sharing schemes.
Findings
Constructed two-Lee-weight codes over ring $R_k$.
Derived optimal binary two-weight codes via Gray map.
Applied codes to secret sharing schemes.
Abstract
We construct a family of two-Lee-weight codes over the ring which is defined as trace codes with algebraic structure of abelian codes. The Lee weight distribution of the two-weight codes is given. Taking the Gray map, we obtain optimal abelian binary two-weight codes by using the Griesmer bound. An application to secret sharing schemes is also given.
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Taxonomy
TopicsCoding theory and cryptography · Cooperative Communication and Network Coding · graph theory and CDMA systems