GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets
<|reference_start|>GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets: Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2^m), where m>0 cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to increment the code dimension by adding more idempotents and so steadily decrease the sparseness of the parity-check matrix. We show that the constructed codes can achieve performance very close to the sphere-packing-bound constrained for binary transmission.<|reference_end|>
@article{tjhai2005gf(2^m),
    title={GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets},
    author={C. Tjhai, M. Tomlinson, R. Horan, M. Ambroze and M. Ahmed},
    journal={arXiv preprint arXiv:cs/0502037},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0502037},
    primaryClass={cs.IT math.IT}
}