A transform theory for a class of group-invariant codes
A binary cyclic code of length of n can be defined by a set of parity-check equations that is invariant under the additive cyclic group generated by A:i to i+1 modulo n. A class of quasicyclic codes that have parity-check equations invariant under the group generated by a subgroup of A and a subgrou...
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| Veröffentlicht in: | IEEE transactions on information theory 1988-07, Vol.34 (4), p.725-775 |
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| container_title | IEEE transactions on information theory |
| container_volume | 34 |
| creator | Tanner, R.M. |
| description | A binary cyclic code of length of n can be defined by a set of parity-check equations that is invariant under the additive cyclic group generated by A:i to i+1 modulo n. A class of quasicyclic codes that have parity-check equations invariant under the group generated by a subgroup of A and a subgroup of the multiplicative group M:i to 2/sup k/i modulo n is studied in detail. The Fourier transform transforms the action of the additive group, and a linearized polynomial transform transforms the action of the multiplicative group. The form of the transformed code equations permits a BCH-like bound on the minimum distance of the code. The techniques are illustrated by the construction of several codes that are decodable by the Berlekamp-Massey algorithm and that have parameters that approach or surpass those of the best codes known.< > |
| doi_str_mv | 10.1109/18.9772 |
| format | Article |
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| ispartof | IEEE transactions on information theory, 1988-07, Vol.34 (4), p.725-775 |
| issn | 0018-9448 1557-9654 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_28718598 |
| source | IEEE Electronic Library (IEL) |
| subjects | Decoding Electronic circuits Equations Error correction codes Feedback Fourier transforms Information theory Parity check codes Polynomials Shift registers |
| title | A transform theory for a class of group-invariant codes |
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