Ten Good Rate (m-r) /pm Binary Quasi-Cyclic Codes

Quasi-Cyclic: (QC) codes are a generalization of cyclic codes whereby a cyclic shift of a codeword by p positions results in another codeword. The class of QC codes is of interest because it contains many of the best known binary linear codes. The results presented here reinforce the statement that ‘Quasi-Cyclic codes are good’. The blocklength, n, of a QC code is a multiple of p , n = mp. Many of the results on QC codes presented in the literature concern those for which a generator matrix can be constructed from m x m circulant matrices, (with a suitable permutation of coordinates). In this case the generator matrix can be represented as