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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Bibliographic Details
Published in:IEEE transactions on information theory 1991-03, Vol.37 (2), p.337-342
Main Authors: Castagnoli, G., Massey, J.L., Schoeller, P.A., von Seemann, N.
Format: Article
Language:English
Subjects:
Block codes
Error correction codes
Galois fields
H infinity control
Helium
Information processing
Information theory
Parity check codes
Signal processing
Vectors
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Summary: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.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.75249