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Description
Two linear codes are equivalent if there exists a monomial matrix that transforms one to the other. The problem of finding a monomial transformation from one code to another underlies the Linear Equivalence Signature Scheme (LESS). An automorphism of a linear code is a monomial matrix which fixes the code. When a code has a large number of automorphisms, it is easier to solve the linear code equivalence problem; thus, it is desirable for cryptography to have codes with as few automorphisms as possible. A code with the smallest possible number of automorphisms is called rigid.
Prior results show that almost all binary codes of dimension k and length 2k are rigid as k goes to infinity. We extend this result to arbitrary finite fields of characteristic 2.