A class of invertible circulant matrices for QC-LDPC codes

This paper presents a new class of easily invertible circulant matrices, defined by exploiting the isomorphism from the ring M
_n
of n times n circulant matrices over GF(p) to the ring R
_n
= GF(p)[x]/(x
ⁿ
- 1) of the polynomials modulo (x
ⁿ
- 1). Such class contains matrices free of 4-length cycles that, if sparse, can be included in the parity check matrix of QC-LDPC codes. Bounds for the weight of their inverses are also determined, that are useful for designing sparse generator matrices for these error correcting codes.