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 language | English |
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Article number | 102013 |
Journal | Finite Fields and their Applications |
Volume | 80 |
DOIs | |
State | Published - Jun 2022 |
Keywords
- Cyclic codes
- Roos bound
- Skew-cyclic codes
- Sum-rank metric
- Tensor product codes