1986/11/01 by K. Abdel-Ghaffar, Khaled Abdel-Ghaffar, R. McEliece +4 · 1 citation
Computer Science · #Coding theory and cryptography #Quantum-Dot Cellular Automata #Cryptography and Data Security
paper · doi:10.1109/tit.1986.1057242
It is shown that for each integer <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b ≥ 1</tex> infinitely many optimum cyclic <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> -burst-correcting codes exist, i.e., codes whose length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> , redundancy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</tex> , and burst-correcting capability <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</tex> , satisfy <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n = 2r-b+1 - 1</tex> . Some optimum codes for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b = 3, 4</tex> , and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">5</tex> are also studied in detail.