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On matrices potentially useful for tree codes
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SYSNO ASEP 0546790 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title On matrices potentially useful for tree codes Author(s) Pudlák, Pavel (MU-W) RID, SAI Article number 106180 Source Title Information Processing Letters. - : Elsevier - ISSN 0020-0190
Roč. 174, March (2022)Number of pages 7 s. Language eng - English Country NL - Netherlands Keywords theory of computation ; matrix ; tree code ; finite field ; singleton bound Subject RIV BA - General Mathematics OECD category Pure mathematics R&D Projects GX19-27871X GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support MU-W - RVO:67985840 UT WOS 000701816300001 EID SCOPUS 85122595710 DOI 10.1016/j.ipl.2021.106180 Annotation Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct asymptotically good tree codes and (2) a random block-triangular matrix over a field of quadratic size satisfies this property. We will also show that a generalization of this randomized construction yields codes over quadratic size fields for which the sum of the rate and minimum relative distance gets arbitrarily close to 1. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2023 Electronic address https://doi.org/10.1016/j.ipl.2021.106180
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