3 years ago

Three-weight ternary linear codes from a family of cyclic difference sets

Zhengchun Zhou

Abstract

Linear codes with a few weights have applications in data storage systems, secret sharing schemes, and authentication codes. Recently, Ding (IEEE Trans. Inf. Theory 61(6):3265–3275, 2015) proposed a class of ternary linear codes with three weights from a family of cyclic difference sets in \(({\mathbb {F}}_{3^m}^*/{\mathbb {F}}_{3}^*,\times )\) , where \(m=3k\) and k is odd. One objective of this paper is to construct ternary linear codes with three weights from cyclic difference sets in \(({\mathbb {F}}_{3^m}^*/{\mathbb {F}}_{3}^*,\times )\) derived from the Helleseth–Gong functions. This construction works for any positive integer \(m=sk\) with an odd factor \(s\ge 3\) , and thus leads to three-weight ternary linear codes with more flexible parameters than earlier ones mentioned above. Another objective of this paper is to determine the weight distribution of the proposed linear codes.

Publisher URL: https://link.springer.com/article/10.1007/s10623-017-0454-1

DOI: 10.1007/s10623-017-0454-1

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