Cyclic Codes

In Section 4.5 we defined the automorphism group Aut(C) of a code C. Corresponding to this group there is a group of permutation matrices. Sometimes the definition of Aut(C) is extended by replacing permutation matrices by monomial matrices, i.e. matrices for which the nonzero entries correspond to a permutation matrix. In both cases we are interested in the group of permutations. In this chapter we shall study linear codes for which the automorphism group contains the cyclic group of order n, where n is the word length.