On transitive uniform partitions of F^n into binary Hamming codes

04/02/2019

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by   Faina I. Solov'eva, et al.

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We investigate transitive uniform partitions of the vector space F^n of dimension n over the Galois field GF(2) into cosets of Hamming codes. A partition P^n= {H_0,H_1+e_1,...,H_n+e_n} of F^n into cosets of Hamming codes H_0,H_1,...,H_n of length n is said to be uniform if the intersection of any two codes H_i and H_j, i,j∈{0,1,...,n } is constant, here e_i is a binary vector in F^n of weight 1 with one in the ith coordinate position. For any n=2^m-1, m>4 we found a class of nonequivalent 2-transitive uniform partitions of F^n into cosets of Hamming codes.