On matrices potentially useful for tree codes

0546790 - MÚ 2023 RIV NL eng J - Journal Article
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
R&D Projects: GA ČR(CZ) GX19-27871X
Institutional support: RVO:67985840
Keywords : theory of computation * matrix * tree code * finite field * singleton bound
OECD category: Pure mathematics
Impact factor: 0.5, year: 2022
Method of publishing: Limited access
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.
Permanent Link: http://hdl.handle.net/11104/0323169