On matrices potentially useful for tree codes

0546790 - MÚ 2023 RIV NL eng J - Článek v odborném periodiku
Pudlák, Pavel
On matrices potentially useful for tree codes.
Information Processing Letters. Roč. 174, March (2022), č. článku 106180. ISSN 0020-0190. E-ISSN 1872-6119
Grant CEP: GA ČR(CZ) GX19-27871X
Institucionální podpora: RVO:67985840
Klíčová slova: theory of computation * matrix * tree code * finite field * singleton bound
Obor OECD: Pure mathematics
Impakt faktor: 0.5, rok: 2022
Způsob publikování: Omezený přístup
https://doi.org/10.1016/j.ipl.2021.106180

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.
Trvalý link: http://hdl.handle.net/11104/0323169