New Family of Linear 3-Erasure Correcting Block Codes with Possible Application in Storage Systems

Authors

  • Peter Farkaš Institute of Multimedia ICT, FEI STU, Ilkovičova 3, 812 19 Bratislava, Slovakia & Institute of Applied Informatics, Faculty of Informatics, Pan-European University, Tematínska 10, 851 05 Bratislava, Slovakia
  • Katarína Farkašová Institute of Multimedia ICT, FEI STU, Ilkovičova 3, 812 19 Bratislava, Slovakia
  • Frederik Pavelka Institute of Multimedia ICT, FEI STU, Ilkovičova 3, 812 19 Bratislava, Slovakia
  • Martin Rakús Institute of Multimedia ICT, FEI STU, Ilkovičova 3, 812 19 Bratislava, Slovakia

Keywords:

Erasure correcting code, linear block code, Vandermonde matrix, parity check matrix, decoding

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.

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Published

2025-04-30

How to Cite

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). Retrieved from https://www.cai.sk/ojs/index.php/cai/article/view/6928

Issue

Vol. 44 No. 2 (2025): Computing and Informatics

Section

Articles