MDS linear codes with one dimensional hull

12/21/2020

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by   Lin Sok, et al.

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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.