On repeated-root cyclic codes
A parity-check matrix for a q-ary repeated-root cyclic code is derived using the Hasse derivative. Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-...
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| Veröffentlicht in: | IEEE transactions on information theory 1991-03, Vol.37 (2), p.337-342 |
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| container_title | IEEE transactions on information theory |
| container_volume | 37 |
| creator | Castagnoli, G. Massey, J.L. Schoeller, P.A. von Seemann, N. |
| description | A parity-check matrix for a q-ary repeated-root cyclic code is derived using the Hasse derivative. Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-root cyclic codes of lengths up to n=62 are shown to contain the largest known number of codewords for their given length and minimum distance. The relative minimum distance d/sub min//n of q-ary repeated-root cyclic codes of rate r>or=R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity. It is further shown that repeated-root cycle codes cannot be asymptotically better than simple-root cyclic codes.< > |
| doi_str_mv | 10.1109/18.75249 |
| format | Article |
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Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-root cyclic codes of lengths up to n=62 are shown to contain the largest known number of codewords for their given length and minimum distance. The relative minimum distance d/sub min//n of q-ary repeated-root cyclic codes of rate r>or=R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity. 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Then the minimum distance of a q-ary repeated-root cyclic code is expressed in terms of the minimum distance of a certain simple-root cyclic code. With the help of this result, several binary repeated-root cyclic codes of lengths up to n=62 are shown to contain the largest known number of codewords for their given length and minimum distance. The relative minimum distance d/sub min//n of q-ary repeated-root cyclic codes of rate r>or=R is proven to tend to zero as the largest multiplicity of a root of the generator g(x) increases to infinity. It is further shown that repeated-root cycle codes cannot be asymptotically better than simple-root cyclic codes.< ></abstract><pub>IEEE</pub><doi>10.1109/18.75249</doi><tpages>6</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | IEEE transactions on information theory, 1991-03, Vol.37 (2), p.337-342 |
| issn | 0018-9448 1557-9654 |
| language | eng |
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| source | IEEE Electronic Library (IEL) |
| subjects | Block codes Error correction codes Galois fields H infinity control Helium Information processing Information theory Parity check codes Signal processing Vectors |
| title | On repeated-root cyclic codes |
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