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Error correcting codes from permutation groups

permutation of n symbols, so the length and alphabet size are both equal to n; codes with larger alphabet. Bailey, Error- correcting codes from permutation groups, Discrete Math. A N ( n, k) error- correcting code over GF ( q) is a k- di- mensional subspace V of GF ( 4) “. An automorphism of v is a monomial permutation of the coordinate set which leaves V invariant. The set of all automorphisms forms a group under. We replace the usual setting for error- correcting codes ( i. vector spaces over fi- nite fields) with that of permutation groups. We give an algorithm which uses a combinatorial structure which we call an uncovering- by- bases,. permutation groups obtained from symmetric generators ( as 2- modular primitive permutation representation) of some finite simple groups as error- correcting codes. We also determine binary linear codes arising from specific. Thus, every group of cells induces a permutation, which is derived by the. under the setup of permutations for the rank modulation scheme; see e. [ 1], [ 6], [ 16].

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    Groups error correcting

    that are derived from error- correcting codes for permutations while the second. Kendall tau distance, rank permutation codes. Various metric functions on the symmetric group Sn have been considered. error- correcting rank permutation codes. WEIGHT- PRESERVING. We replace the traditional setting for error- correcting codes ( i. linear codes) with that of permutation groups, with permutations in list form as the codewords. We introduce a decoding algorithm for these codes, which uses the. This is also related to error correction: if more errors occur than the covering radius, then nearest- neighbour decoding will certainly be wrong! Much is known about this parameter for codes, but comparatively little for permutation groups. Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error- correcting codes, groups are here considered that act transitively on the pairs of coordinates and. vector spaces over finite fields) with that of permutation groups.