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\iteman{io-port 05845399}
\itemau{Hurley, Paul; Hurley, Ted}
\itemti{Codes from zero-divisors and units in group rings.}
\itemso{Int. J. Inf. Coding Theory 1, No. 1, 57-87 (2009).}
\itemab
Self-dual codes or low-density parity-check (LDPC) codes can be described as zero-divisor or unit-delivered codes within group rings. The authors construct these codes, establishing the isomorphism between the group rings and matrix rings. This enables them to study the zero-divisor and unit derived codes in terms of matrices and derive their generators and check matrices. Their method gives a possibility to construct codes in group rings with many types of the underlying rings (e.g. integers, matrix rings, group rings). The presented codes are submodules of the group ring. They also discuss conditions under which codes are ideals of group rings. A number of examples for unit-derived and zero divisor codes are also presented.
\itemrv{Piroska Lakatos (Debrecen)}
\itemcc{}
\itemut{group rings; coding theory; group algebras; LDPC; self-duality; unit-derived codes; zero-divisor codes; low-density parity-check}
\itemli{doi:10.1504/IJICOT.2009.024047}
\end