Distance Properties of Group Codes for the Gaussian Channel
Jan F. Blake · SIAM Journal on Applied Mathematics · 1972
Some distance properties of group codes for the Gaussian channel introduced by Slepian (1968) are examined. The concept of a full homogeneous component is introduced and optimal vectors for such group representations are found. The results are applied to the symmetric and Mathieu groups which are found to yield exceptional simplex-like codes with code size larger than the corresponding simplex code. Finally, a theorem on the representation of a doubly transitive permutation group is used to solve the optimal vector problem for the irreducible representation of dimension $n - 1$ of the symmetric group of degree n.