2022/10/11 by Meng Cao, Jing Yang, Cao, Meng +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Computer and information sciences #Finite Group Theory Research #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2210.05551
openalex publication_date 2022/10/11 · openalex created_date 2022/10/14 · openalex updated_date 2026/07/28
Let SLAut(\mathbbFqn) denote the group of all semilinear isometries on \mathbbFqn, where q=pe is a prime power. In this paper, we investigate general properties of linear codes associated with σ duals for σ\inSLAut(\mathbbFqn). We show that the dimension of the intersection of two linear codes can be determined by generator matrices of such codes and their σ duals. We also show that the dimension of σ hull of a linear code can be determined by a generator matrix of it or its σ dual. We give a characterization on σ dual and σ hull of a matrix-product code. We also investigate the intersection of a pair of matrix-product codes. We provide a necessary and sufficient condition under which any codeword of a generalized Reed-Solomon (GRS) code or an extended GRS code is contained in its σ dual. As an application, we construct eleven families of q-ary MDS codes with new ℓ-Galois hulls satisfying 2(e-ℓ)| e, which are not covered by the latest papers by Cao (IEEE Trans. Inf. Theory 67(12), 7964-7984, 2021) and by Fang et al. (Cryptogr. Commun. 14(1), 145-159, 2022) when ℓ≠ (e)/(2).