On the minimum hamming distance of the pm-ary image of linear block codes over the finite chain ring Fpm + uFpm + ... + ur-1Fpm, ur = 0./
By: Palacio, Jane D.
Contributor(s): Sison, Virgilio P | Lampos, John Mark T.
Description: vol. 7, 1 table, refs.ISSN: 1908-1995.Other title: Philippine Computing Journal.Subject(s): FINITE CHAIN RING | PM-ARY IMAGE | DISTANCE BOUNDSDDC classification: 050/P17 Summary: Let Fpm denote the finite field with pm elements where p is a prime. In this paper, linear block codes over Fpm are considered as images of linear block codes over the finite chain ring R(pm, r) = Fpm + uFpm + ... +ur-1Fpm, where ur + 0 and m, r E N. An Fpm linear map is defined from R (pm, r)n to Frnpm. Bounds on the minimum Hamming distance of the resultant codes are derived. These bounds largely depend on the minimum Hamming distance of the linear block code, the average value of the homogeneous weight on the residue field Fpm and the nilpotency index of the ring. A code meeting these bounds whose image is the extended binary Hamming code of order 3 is also given.| Item type | Current location | Collection | Call number | Status | Date due | Barcode |
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Let Fpm denote the finite field with pm elements where p is a prime. In this paper, linear block codes over Fpm are considered as images of linear block codes over the finite chain ring R(pm, r) = Fpm + uFpm + ... +ur-1Fpm, where ur + 0 and m, r E N. An Fpm linear map is defined from R (pm, r)n to Frnpm. Bounds on the minimum Hamming distance of the resultant codes are derived. These bounds largely depend on the minimum Hamming distance of the linear block code, the average value of the homogeneous weight on the residue field Fpm and the nilpotency index of the ring. A code meeting these bounds whose image is the extended binary Hamming code of order 3 is also given.
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