Sum-rank product codes and bounds on the minimum distance

Gianira N. Alfarano, F. J. Lobillo, Alessandro Neri, Antonia Wachter-Zeh

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

The tensor product of one code endowed with the Hamming metric and one endowed with the rank metric is analyzed. This gives a code which naturally inherits the sum-rank metric. Specializing to the product of a cyclic code and a skew-cyclic code, the resulting code turns out to belong to the recently introduced family of cyclic-skew-cyclic codes. A group theoretical description of these codes is given, after investigating the semilinear isometries in the sum-rank metric. Finally, a generalization of the Roos and the Hartmann-Tzeng bounds for the sum rank-metric is established, as well as a new lower bound on the minimum distance of one of the two codes constituting the product code.

Original languageEnglish
Article number102013
JournalFinite Fields and their Applications
Volume80
DOIs
StatePublished - Jun 2022

Keywords

  • Cyclic codes
  • Roos bound
  • Skew-cyclic codes
  • Sum-rank metric
  • Tensor product codes

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