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Robert W. Quackenbush - Varieties of binary linear codes

ROBERT W. QUACKENBUSH, Department of Mathematics, University of Manitoba, Winnipeg, Manitoba  R3T 2N2, Canada
Varieties of binary linear codes

A binary linear code is a vector space V over GF(2) with an added unary operation, ', satisfying 0' = 0; x'' = x', and (x' + y )' = x' + y'. This last law exactly expresses the facts that the set of codewords $C :=\{x' \mid x \in V\}$ is a subspace and that ' on any coset of C is a translation by a fixed element. I will discuss the lattice of subvarieties and discuss some connections to classical linear codes, e.g., Hamming codes are closely related to the n-generated free codes in the variety.


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