TY - GEN
T1 - The minimum distance of some binary codes via the newton’s identities
AU - Augot, D.
AU - Charpin, P.
AU - Sendrier, N.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1991.
PY - 1991/1/1
Y1 - 1991/1/1
N2 - In this paper, we give a natural way of deciding whether a given cyclic code contains a word of given weight. The method is based on the manipulation of the locators and of the locator polynomial of a codeword x. Because of the dimensions of the problem, we need to use a symbolic computation software, like Maple or Scratchpad II. The method can be ineffective when the length is too large. The paper contains two parts: In the first part we will present the main definitions and properties we need. In the second part, we will explain how to use these properties, and, as illustration, we will prove the three following facts: The dual of the BCH code of length 63 and designed distance 9 has true minimum distance 14 (which was already known). The BCH code of length 1023 and designed distance 253 has minimum distance 253. The cyclic codes of length 211, 213, 217, with generator polynomial m1(x) and m7(x) have minimum distance 4 (see [5]).
AB - In this paper, we give a natural way of deciding whether a given cyclic code contains a word of given weight. The method is based on the manipulation of the locators and of the locator polynomial of a codeword x. Because of the dimensions of the problem, we need to use a symbolic computation software, like Maple or Scratchpad II. The method can be ineffective when the length is too large. The paper contains two parts: In the first part we will present the main definitions and properties we need. In the second part, we will explain how to use these properties, and, as illustration, we will prove the three following facts: The dual of the BCH code of length 63 and designed distance 9 has true minimum distance 14 (which was already known). The BCH code of length 1023 and designed distance 253 has minimum distance 253. The cyclic codes of length 211, 213, 217, with generator polynomial m1(x) and m7(x) have minimum distance 4 (see [5]).
UR - https://www.scopus.com/pages/publications/84938006364
U2 - 10.1007/3-540-54303-1_119
DO - 10.1007/3-540-54303-1_119
M3 - Conference contribution
AN - SCOPUS:84938006364
SN - 9783540543039
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 65
EP - 73
BT - EUROCODE 1990 - International Symposium on Coding Theory and Applications, Proceedings
A2 - Cohen, Gerard
A2 - Charpin, Pascale
PB - Springer Verlag
T2 - International Symposium on Coding Theory and Applications, EUROCODE 1990
Y2 - 5 November 1990 through 9 November 1990
ER -