Weight distributions of some irreducible cyclic codes
Authors: Robert Segal and Robert L. Ward
Journal: Math. Comp. 46 (1986), 341-354
MSC: Primary 94B15; Secondary 11T71
MathSciNet review: 815855
Full-text PDF Free Access
Abstract: The theory of weight distributions of irreducible cyclic codes over a finite field has been extensively developed by R. J. McEliece and others. We apply that theory to compute the weight enumerators of some binary codes which have hitherto not been possible. In so doing, we correct an error by McEliece and describe his process in somewhat more detail.
- L. D. Baumert and R. J. McEliece, Weights of irreducible cyclic codes, Information and Control 20 (1972), 158–175. MR 497284
- Jessie MacWilliams and Judith Seery, The weight distributions of some minimal cyclic codes, IEEE Trans. Inform. Theory 27 (1981), no. 6, 796–806. MR 650721, DOI https://doi.org/10.1109/TIT.1981.1056420
- Edwin Weiss, Algebraic number theory, McGraw-Hill Book Co., Inc., New York-San Francisco-Toronto-London, 1963. MR 0159805
L. D. Baumert & R. J. McEliece, "Weights of irreducible cyclic codes," Inform. and Control, v. 20, 1972, No. 2, pp. 158-175.
F. Jessie MacWilliams & Judith Seery, "The weight distributions of some minimal cyclic codes," IEEE Trans. Inform. Theory, v. IT-27, 1981, No. 6, pp. 796-806.
Edwin Weiss, Algebraic Number Theory, McGraw-Hill, New York, 1963.