On matrices potentially useful for tree codes

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00546790" target="_blank" >RIV/67985840:_____/22:00546790 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.ipl.2021.106180" target="_blank" >https://doi.org/10.1016/j.ipl.2021.106180</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.ipl.2021.106180" target="_blank" >10.1016/j.ipl.2021.106180</a>

Result language
angličtina
Original language name
On matrices potentially useful for tree codes
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GX19-27871X" target="_blank" >GX19-27871X: Efficient approximation algorithms and circuit complexity</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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