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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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Farkaš et al. (2025) studied this question.
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