Some Bounds on Binary LCD Codes

2017/01/16 by Galvez, Lucky, Kim, Jon-Lark, Lee, Nari +2 · 1 citation
#94B05 #94B65 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1701.04165

Abstract

A linear code with a complementary dual (or LCD code) is defined to be a linear code C whose dual code C^⊥ satisfies C ∩ C^⊥= \ 0\ . Let LCD[n,k] denote the maximum of possible values of d among [n,k,d] binary LCD codes. We give exact values of LCD[n,k] for 1 ≤ k ≤ n ≤ 12. We also show that LCD[n,n-i]=2 for any i≥2 and n≥2ⁱ. Furthermore, we show that LCD[n,k]≤ LCD[n,k-1] for k odd and LCD[n,k]≤ LCD[n,k-2] for k even.

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