Abstract
A construction of a new family of three erasure correcting linear block codes over GF(q) with characteristic two together with their syndrome decoding procedures are presented in this paper. The designed code distance of four was confirmed by demonstrating a decoding algorithm capable of correcting three erasures. The second confirmation was obtained from the weight spectra of selected codes, which were calculated using Krawtchouck polynomials derived from the weight spectra of their dual codes.
Keywords
MSC
58F15, 58F17, 53C35
Cite this article
@article{cai-6928,
author = {Peter Farkaš and Katarína Farkašová and Frederik Pavelka and Martin Rakús},
title = {New Family of Linear 3-Erasure Correcting Block Codes with Possible Application in Storage Systems},
journal = {Computing and Informatics},
volume = {44},
number = {2},
pages = {429--444},
year = {2025},
issn = {1335-9150},
doi = {10.31577/cai_2025_2_429}
}
TY - JOUR AU - Peter Farkaš AU - Katarína Farkašová AU - Frederik Pavelka AU - Martin Rakús TI - New Family of Linear 3-Erasure Correcting Block Codes with Possible Application in Storage Systems JO - Computing and Informatics VL - 44 IS - 2 SP - 429 EP - 444 PY - 2025 SN - 1335-9150 DO - 10.31577/cai_2025_2_429 UR - https://doi.org/10.31577/cai_2025_2_429 KW - Erasure correcting code KW - linear block code KW - Vandermonde matrix KW - parity check matrix KW - decoding ER -
Farkaš, P., Farkašová, K., Pavelka, F., & Rakús, M. (2025). New Family of Linear 3-Erasure Correcting Block Codes with Possible Application in Storage Systems. Computing and Informatics, 44(2), 429–444. https://doi.org/10.31577/cai_2025_2_429