Minimum-weight codewords as generators of generalized Reed-Muller codes

IEEE Transactions on Information Theory

Volumn 46, Issue 6, 2000, Pages 2152-2158

  Ding, Peng ^a   Key, Jennifer D ^a  

^a CLEMSON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CODES (SYMBOLS); ENCODING (SYMBOLS); THEOREM PROVING; VECTORS;

GENERALIZED REED-MULLER CODES; MINIMUM WEIGHT VECTORS;

DIGITAL SIGNAL PROCESSING;

EID: 0034271895     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.868484     Document Type: Article

References (9)

1. E. F. Assmus, Jr. and J. D. Key, Designs and Their Codes, ser. Cambridge Tracts in Mathematics. Cambridge, U.K.: Cambridge Univ. Press, 1992, second printing with corrections, vol. 103, 1993.
2. _, Polynomial codes and finite geometries, in Handbook of Coding Theory, V. S. Pless and W. C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, 1998, pt. 2, vol. 2, ch. 16, pp. 1269-1343.
3. T. Berger and P. Charpin, The automorphism group of generalized Reed-Muller codes, Discr. Math., vol. 117, pp. 1-17, 1993.
4. W. Bosma and J. Cannon, Handbook of Magma Functions. Sydney, Australia: Dept. Math., Univ. Sydney, Nov. 1994.
5. P. Charpin, Open problems on cyclic codes, in Handbook of Coding Theory, V. S. Pless and W. C. Huffman, Eds. Amsterdam, The Netherlands: Elsevier, 1998, pt. 1, vol. 1, ch. 11, pp. 963-1063.
6. P. Delsarte, J. M. Goethals, and F. J. MacWilliams, On generalized Reed-Muller codes and their relatives, Inform. Contr, vol. 16, pp. 40342, 1970.
7. P. Delsarte, On cyclic codes that are invariant under the general linear group, IEEE Trans. Inform. Theory, vol. IT-16, pp. 760-769, Nov. 1970.
8. S. Gao and J. D. Key, Bases of minimum-weight vectors for codes from designs, Finite Fields Appl., vol. 4, pp. 1-15, 1998.
9. B. Mortimer, Some problems on permutation groups: Affine groups and modular permutation representations, Ph.D. dissertation, Westfield College, Univ. London, London, U.K., 1977.