MDS linear codes with one dimensional hull
Abstract
We define the Euclidean hull of a linear code $C$ as the intersection of $C$ and its Euclidean dual $C^\perp$. 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.11247
- arXiv:
- arXiv:2012.11247
- Bibcode:
- 2020arXiv201211247S
- Keywords:
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- Computer Science - Information Theory
- E-Print:
- 10 pages, submitted to IEEE Transactions on Information Theory on June 12, 2020