an algebraic construction of qcldpc codes based on powers of primitive elements in a finite field and free of small etss

An (a; b) elementary trapping set (ets), where a and b denote the size and the number of unsatisfied check nodes in the ets, in uences the performance of low-density parity-check (ldpc) codes. the smallest size of an ets in ldpc codes with column weight 3 and girth 6 is 4. in this paper, we concentrate on a well-known algebraic-based construction of girth-6 qc-ldpc codes based on powers of a primitive element in a nite eld fq. for this structure, we provide the sucient conditions to obtain 3n submatrices of an exponent matrix in constructing girth-6 qc-ldpc codes whose etss have the size of at least 5. for structures on finite field fq, where q is a power of 2, all non-isomorphic 3 x n submatrices of the exponent matrix which yield qc-ldpc codes free of small etss are presented.