Abstract
In this chapter, the algebra of groups ring and matrix rings is used to construct and analyze systems of zero-divisor and unit-derived codes. These codes are more general than codes from ideals (e.g. cyclic codes) in group rings. They expand the space of linear block codes, offering additional flexibility in terms of desired properties as algebraic formulations, while also have readily available generator and check matrices. A primer is presented in the necessary algebra, showing how group rings and certain rings of matrices can be used interchangeably. Then it is shown how the codes may be derived, showing particular cases such as self-dual codes and codes from dihedral group rings.
| Original language | English |
|---|---|
| Title of host publication | Selected Topics in Information and Coding Theory |
| Publisher | World Scientific Publishing Co. |
| Pages | 159-194 |
| Number of pages | 36 |
| ISBN (Electronic) | 9789812837172 |
| ISBN (Print) | 9789812837165 |
| DOIs | |
| Publication status | Published - 1 Jan 2010 |