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Puncturing maximum rank distance codes

Authors
  • Csajbók, Bence1
  • Siciliano, Alessandro2
  • 1 ELTE Eötvös Loránd University, MTA-ELTE Geometric and Algebraic Combinatorics Research Group, Department of Geometry, Pázmány P. stny. 1/C, Budapest, 1117, Hungary , Budapest (Hungary)
  • 2 Università degli Studi della Basilicata, Dipartimento di Matematica, Informatica ed Economia, Potenza, Italy , Potenza (Italy)
Type
Published Article
Journal
Journal of Algebraic Combinatorics
Publisher
Springer US
Publication Date
Aug 14, 2018
Volume
49
Issue
4
Pages
507–534
Identifiers
DOI: 10.1007/s10801-018-0833-3
Source
Springer Nature
Keywords
License
Yellow

Abstract

We investigate punctured maximum rank distance codes in cyclic models for bilinear forms of finite vector spaces. In each of these models, we consider an infinite family of linear maximum rank distance codes obtained by puncturing generalized twisted Gabidulin codes. We calculate the automorphism group of such codes, and we prove that this family contains many codes which are not equivalent to any generalized Gabidulin code. This solves a problem posed recently by Sheekey (Adv Math Commun 10:475–488, 2016).

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