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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
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.
