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.

DOI: 10.1007/s10623-017-0454-1

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