Sequence of Numbers of Linear Codes with Increasing Hull Dimensions

2024/02/02 by Bouyuklieva, Stefka, Bouyukliev, Iliya, Özbudak, Ferruh
#94B05 #Discrete Mathematics (cs.DM) #E.4 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.2402.01255

Abstract

The hull of a linear code C is the intersection of C with its dual code. We present and analyze the number of linear q-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension k and length n≥ 2k the number of all [n,k]_q linear codes with hull dimension l decreases as l increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length n and dimension k, comparing the obtained numbers with the number of all linear codes for the given n and k.

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