Linear MSRD codes with Various Matrix Sizes and Unrestricted Lengths
Abstract
A sum-rank-metric code attaining the Singleton bound is called maximum sum-rank distance (MSRD). MSRD codes have been constructed for some parameter cases. In this paper we construct a linear MSRD code over an arbitrary field ${\bf F}_q$ with various matrix sizes $n_1>n_2>\cdots>n_t$ satisfying $n_i \geq n_{i+1}^2+\cdots+n_t^2$ for $i=1, 2, \ldots, t-1$ for any given minimum sum-rank distance.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2022
- DOI:
- 10.48550/arXiv.2206.02330
- arXiv:
- arXiv:2206.02330
- Bibcode:
- 2022arXiv220602330C
- Keywords:
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- Computer Science - Information Theory
- E-Print:
- 11 pages, no restriction on lengths of codes. arXiv admin note: substantial text overlap with arXiv:2205.13087