Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A classification of the cosets of the Reed-Muller code $ \mathcal{R}(1,6)$


Author: James A. Maiorana
Journal: Math. Comp. 57 (1991), 403-414
MSC: Primary 94B05; Secondary 94-04, 94B35
MathSciNet review: 1079027
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] Elwyn R. Berlekamp and Lloyd R. Welch, Weight distributions of the cosets of the (32,6) Reed-Muller code, IEEE Trans. Information Theory IT-18 (1972), 203–207. MR 0396054 (52 #16844)
  • [2] F. J. MacWilliams and N. J. A. Sloane, The theory of error-correcting codes, North-Holland, New York, 1977.
  • [3] 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 (43 #6000)
  • [4] Recent developments in switching theory, Edited by Amar Mukhopadhyay, Academic Press, New York, 1971. MR 0278844 (43 #4572)
  • [5] 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), Amer. Math. Soc., Providence, R.I., 1971, pp. 191–195. SIAM-AMS Proc., Vol. IV. MR 0338135 (49 #2901)
  • [6] -, Computation with permutation groups, Proc. Second Sympos. on Symbolic and Algebraic Manipulation, Assoc. Comput. Mach., New York, 1971.

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 94B05, 94-04, 94B35

Retrieve articles in all journals with MSC: 94B05, 94-04, 94B35


Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1991-1079027-8
PII: S 0025-5718(1991)1079027-8
Article copyright: © Copyright 1991 American Mathematical Society