This paper investigates the theory of sum-rank-metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory of sum-rank-metric codes is also explored, showing that MSRD codes (the sum-rank analogue of MDS codes) dualize to MSRD codes only if all matrix blocks have the same number of columns. In the latter case, duality considerations lead to an upper bound on the number of blocks for MSRD codes. The paper also contains various constructions of sum-rank-metric codes for variable block sizes, illustrating the possible behaviours of these objects with respect to bounds, existence, and duality properties.
|Number of pages||20|
|Journal||IEEE Transactions on Information Theory|
|State||Published - Oct 2021|
Bibliographical noteFunding Information:
Manuscript received October 6, 2020; accepted March 8, 2021. Date of publication April 20, 2021; date of current version September 15, 2021. The work of Heide Gluesing-Luerssen was supported in part by the Simons Foundation under Grant #422479. Eimear Byrne is with the School of Mathematics and Statistics, University College Dublin, Dublin 4, Ireland (e-mail: firstname.lastname@example.org). Heide Gluesing-Luerssen is with the Department of Mathematics, University of Kentucky, Lexington, KY 40506 USA (e-mail: email@example.com). Alberto Ravagnani is with the Department of Mathematics and Computer Science, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands (e-mail: firstname.lastname@example.org). Communicated by G. Matthews, Associate Editor for Coding Theory. Color versions of one or more figures in this article are available at https://doi.org/10.1109/TIT.2021.3074190. Digital Object Identifier 10.1109/TIT.2021.3074190
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- MSRD code
- MacWilliams identity
- Sum-rank-metric code
- asymptotic bound
- code construction
ASJC Scopus subject areas
- Information Systems
- Computer Science Applications
- Library and Information Sciences