Conference Publication Details
Mandatory Fields
Hurley, P,Hurley, T,
Module codes in group rings
2007 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS, VOLS 1-7
2007
July
Published
1
()
Optional Fields
1981
A new construction method for codes using encodings from group rings is presented. They consist primarily of two types, zero-divisor and unit-derived codes. Previous codes from group rings focused on ideals; e.g. cyclic codes are ideals in the group ring over a cyclic group. The fresh focus is on the encodings themselves, which only under very limited conditions result in ideals.Using an isomorphism between group rings and a certain well-defined ring of matrices, equivalent matrix codes are established with resulting generator and check matrices.Group rings are a fruitful source of units and zero-divisors from which new codes result. Many code properties may more easily be expressed in terms of group ring properties.
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