automorphism group (linear code)
This definition looks quite complicated, but since is , it really just means that is the linear code obtained from by permuting its coordinates and then multiplying each coordinate with some nonzero element from .
Two linear codes lying in the same orbit with respect to this action are said to be equivalent. The isotropy subgroup of is its automorphism group, denoted by . The elements of are the automorphisms of .
Sometimes one is only interested in the action of the permutation matrices on . The permutation matrices form a subgroup of and the resulting subgroup of the automorphism group of a linear code is called the permutation group. In the case of binary codes, this doesn’t make any difference, since the finite field contains only one nonzero element.
|Title||automorphism group (linear code)|
|Date of creation||2013-03-22 15:18:40|
|Last modified on||2013-03-22 15:18:40|
|Last modified by||GrafZahl (9234)|