Abstract
Linear error-block codes were introduced in 2006 as a generalization of linear block codes. In this paper we construct two new families of perfect binary linear error-block codes of \( \pi \)-distance 3, namely, \([n_1]\ldots [n_t][2]^s\) (where \( t\ge 1 \)), and \([n_1][n_t][3]^s\) (where \( t= 1\) or \(t=2\)), we also introduce the notions of Hamming and Simplex linear error-block codes, and we give a method to construct Hamming LEB codes from its parity check matrix. We also prove that Hamming LEB codes are perfect, and the constructed perfect codes are Hamming.
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Belabssir, S., Ayebie, E.B., Souidi, E.M. (2019). Perfect, Hamming and Simplex Linear Error-Block Codes with Minimum \(\pi \)-distance 3. In: Carlet, C., Guilley, S., Nitaj, A., Souidi, E. (eds) Codes, Cryptology and Information Security. C2SI 2019. Lecture Notes in Computer Science(), vol 11445. Springer, Cham. https://doi.org/10.1007/978-3-030-16458-4_17
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DOI: https://doi.org/10.1007/978-3-030-16458-4_17
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