Perfect, Hamming and Simplex Linear Error-Block Codes with Minimum \(\pi \)-distance 3

  • Soukaina Belabssir
  • Edoukou Berenger Ayebie
  • El Mamoun SouidiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11445)


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.


Linear error-block codes Simplex codes Hamming code Hamming bound and perfect codes 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Soukaina Belabssir
    • 1
  • Edoukou Berenger Ayebie
    • 1
  • El Mamoun Souidi
    • 1
    Email author
  1. 1.Faculty of Sciences, Laboratory of Mathematics, Computer Science, Applications and Information SecurityMohammed V University in RabatRabatMorocco

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