propelinear

English

Etymology

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Adjective

propelinear (not comparable)

1. (mathematics) A code C is propelinear if, for every codeword x in C, there exists a coordinate permutation P_x such that x + P_x (C) = C and, for any codewords x, y, z, and c in C, if x + P_x(y) = z, then P_z(c) is the composition of the permutations P_x and P_y(c).
   • 2015, I. Yu. Mogilnykh, “On the extention^[sic] of propelinear structures of Nordstrom-Robinson code to Hamming code”, in arXiv‎^[1]:

     In the paper a classification of the propelinear structures on the Nordstrom-Robinson code is obtained and the question of extension of these structures to propelinear structures of the Hamming code, that contains the Nordstrom-Robinson code.