Evaluation codes and their basic parameters

Evaluation codes and their basic parameters

The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed–Muller-type codes, and we determine the minimum distance of toric cod...

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Veröffentlicht in:Designs, codes, and cryptography codes, and cryptography, 2021-02, Vol.89 (2), p.269-300
Hauptverfasser: Jaramillo, Delio, Vaz Pinto, Maria, Villarreal, Rafael H.
Format: Artikel
Sprache:eng
Schlagworte:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Lower bounds
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Zusammenfassung:The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed–Muller-type codes, and we determine the minimum distance of toric codes over hypersimplices, and the 1st and 2nd generalized Hamming weights of squarefree evaluation codes.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-020-00818-8