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MDS linear codes with one dimensional hull

2020/12/21 by Lin Sok, Sok, Lin · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Wireless Communication Techniques #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #cs.IT #math.IT

paper · pdf · doi:10.48550/arxiv.2012.11247

10 pages, submitted to IEEE Transactions on Information Theory on June 12, 2020

arxiv created 2020/12/21 · openalex publication_date 2020/12/21 · arxiv updated 2020/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define the Euclidean hull of a linear code C as the intersection of C and its Euclidean dual C^⊥. The hull with low dimensions gets much interest due to its crucial role in determining the complexity of algorithms for computing the automorphism group of a linear code and checking permutation equivalence of two linear codes. It has been recently proved that any q-ary [n,k] linear code with q>3 gives rise to a linear code with the same parameters and having zero dimensional Euclidean hull, which is known as a linear complementary dual code. This paper aims to explore explicit constructions of families of MDS linear codes with one dimensional Euclidean hull. We obtain several classes of such codes.

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