GRÖBNER BASIS TECHNIQUES TO COMPUTE WEIGHT DISTRIBUTIONS OF SHORTENED CYCLIC CODES
Abstract
Using Gröbner techniques, we can exhibit a method to get the distance and weight distribution of cyclic codes and shortened cyclic codes, improving earlier similar results for the distance of cyclic codes.
References
- IEEE Trans. Inform. Theory 38(4), 1382 (1992), DOI: 10.1109/18.144721. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 52(8), 3700 (2006), DOI: 10.1109/TIT.2006.876240. Crossref, Web of Science, Google Scholar
A. M. Bigatti , Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (Springer Verlag, San Juan, PR, 1993) pp. 76–88. Crossref, Google Scholar- Appl. Algebra Engrg. Comm. Comput. 13(3), 209 (2002), DOI: 10.1007/s002000200097. Crossref, Web of Science, Google Scholar
- Duke Math. J. 24, 37 (1957), DOI: 10.1215/S0012-7094-57-02406-7. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 40, 1654 (1994), DOI: 10.1109/18.333885. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 12(3), 404 (1966), DOI: 10.1109/TIT.1966.1053892. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 43(4), 1364 (1997), DOI: 10.1109/18.605611. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 38(2), 504 (1992), DOI: 10.1109/18.119712. Crossref, Web of Science, Google Scholar
- T. Fujiwara and T. Kasami, The weight distributions of (256, k) extended binary primitive BCH codes with k ≤ 63 and k ≥ 207, Technical Report of IEICE, IT97-46 (1997-09), pp. 29–33 . Google Scholar
- M. Giorgetti and M. Sala, A commutative algebra approach to linear codes, BCRI Preprint Series, No. 59, available at http://www.bcri.ucc.ie . Google Scholar
- IEEE Trans. Inform. Theory 20(1), 129 (1974), DOI: 10.1109/TIT.1974.1055149. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 40(3), 951 (1994), DOI: 10.1109/18.335910. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 18, 824 (1972), DOI: 10.1109/TIT.1972.1054903. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 45(1), 251 (1999), DOI: 10.1109/18.746800. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 45(1), 247 (1999), DOI: 10.1109/18.746798. Crossref, Web of Science, Google Scholar
- MAGMA, http://www.maths.usyd.edu.au:8000/u/magma/ . Google Scholar
- MEDICIS, http://www.medicis.polytechnique.fr . Google Scholar
- J. Symbolic Comput. 35(2), 177 (2003), DOI: 10.1016/S0747-7171(02)00131-1. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 40(6), 1894 (1994), DOI: 10.1109/18.340464. Crossref, Web of Science, Google Scholar
- IEEE Trans. Inform. Theory 53(3), 1095 (2007), DOI: 10.1109/TIT.2006.889465. Crossref, Web of Science, Google Scholar
- J. Pure Appl. Algebra 200, 191 (2005), DOI: 10.1016/j.jpaa.2004.12.027. Crossref, Web of Science, Google Scholar
- Appl. Algebra Engrg. Comm. Comput. 13(2), 137 (2002), DOI: 10.1007/s002000200096. Crossref, Web of Science, Google Scholar
- M. Sala, Gröbner bases, accelerator polynomials and binary cyclic codes with coincident distance, Dept. of Math. of Univ. of Pisa (2002), preprint . Google Scholar
- IEEE Trans. Inform. Theory 46(6), 2235 (2000), DOI: 10.1109/18.868496. Crossref, Web of Science, Google Scholar