TY - GEN
T1 - Algebraic characterization of minimum weight codewords of cyclic codes
AU - Augot, Daniel
PY - 1994/1/1
Y1 - 1994/1/1
N2 - We consider primitive cyclic codes of length n over GF(q), where n=q m-1, and for any such code with defining set I(C), we define a system of algebraic equations, SI(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system SI(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.
AB - We consider primitive cyclic codes of length n over GF(q), where n=q m-1, and for any such code with defining set I(C), we define a system of algebraic equations, SI(C)(w), constructed with the Newton identities for the weight w. We prove that algebraic solutions of this system are in correspondence with all codewords of C of weight lower than w. To deal effectively with the system SI(C)(w), we compute a Groebner basis of this system, which gives pertinent information on minimum weight codewords. A few examples are given.
UR - https://www.scopus.com/pages/publications/84894317963
U2 - 10.1109/ISIT.1994.394925
DO - 10.1109/ISIT.1994.394925
M3 - Conference contribution
AN - SCOPUS:84894317963
SN - 0780320158
SN - 9780780320154
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 46
BT - Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 1994 IEEE International Symposium on Information Theory, ISIT 1994
Y2 - 27 June 1994 through 1 July 1994
ER -