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

Peter Farkaš

Institute of Multimedia Information and Communication Technologies Faculty of Electrical Engineering and Information Technology Slovak University of Technology in Bratislava Ilkovičova 3, 812 19 Bratislava, Slovakia & Institute of Applied Informatics Faculty of Informatics Pan-European University, Slovakia 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

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

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

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.

mathematics subject classification 2000: 58F15, 58F17, 53C35

reference: Vol. 44, 2025, No. 2, pp. 429–444

doi: 10.31577/cai_2025_2_429

Computing and Informatics

formerly Computers and Artificial Intelligence

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