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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

A classification of the cosets of the Reed-Muller code $\mathcal {R}(1,6)$
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by James A. Maiorana PDF
Math. Comp. 57 (1991), 403-414 Request permission

Abstract:

The weight distribution of a coset of a Reed-Muller code $\mathcal {R}(1,m)$ is invariant under a large transformation group consisting of all affine rearrangements of a vector space with dimension m. We discuss a general algorithm that produces an ordered list of orbit representatives for this group action. As a by-product the procedure finds the order of the symmetry group of a coset. With $m = 6$ we can implement the algorithm on a computer and find that there are 150357 equivalence classes. These classes produce 2082 distinct weight distributions. Their symmetry groups have 122 different orders.
References
  • Elwyn R. Berlekamp and Lloyd R. Welch, Weight distributions of the cosets of the $(32,\,6)$ Reed-Muller code, IEEE Trans. Inform. Theory IT-18 (1972), 203–207. MR 396054, DOI 10.1109/tit.1972.1054732
    • F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, North-Holland, New York, 1977.
  • Michael A. Harrison, Counting theorems and their applications to classification of switching functions, Recent Developments in Switching Theory, Academic Press, New York, 1971, pp. 85–120. MR 0280279
  • Amar Mukhopadhyay (ed.), Recent developments in switching theory, Academic Press, New York-London, 1971. MR 0278844
  • Charles C. Sims, Determining the conjugacy classes of a permutation group, Computers in algebra and number theory (Proc. SIAM-AMS Sympos. Appl. Math., New York, 1970) SIAM-AMS Proc., Vol. IV, Amer. Math. Soc., Providence, R.I., 1971, pp. 191–195. MR 0338135
    • —, Computation with permutation groups, Proc. Second Sympos. on Symbolic and Algebraic Manipulation, Assoc. Comput. Mach., New York, 1971.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Math. Comp. 57 (1991), 403-414
  • MSC: Primary 94B05; Secondary 94-04, 94B35
  • DOI: https://doi.org/10.1090/S0025-5718-1991-1079027-8
  • MathSciNet review: 1079027