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- W2898024343 abstract "Partial syndrome matrices and weak-locator polynomials have received considerable attention in recent years due to their applications in decoding cyclic codes. The technical contribution of this paper is threefold: 1) cyclic codes can be decoded by the newly proposed partial syndrome matrices, which generalize the previously known results on the determination of error positions; 2) a new type of polynomial associated with error locations, called radical-locator polynomial , is defined, which includes the weak-locator polynomial as a special case; and 3) a novel class of matrices with many zero entries, called row-echelon partial syndrome matrices , is presented, based on the Newton identities, for efficiently decoding cyclic codes. It is also shown that the radical-locator polynomials can be obtained from the determinants of the above-mentioned (row-echelon) partial syndrome matrices." @default.
- W2898024343 created "2018-10-26" @default.
- W2898024343 creator A5088089404 @default.
- W2898024343 date "2019-06-01" @default.
- W2898024343 modified "2023-10-08" @default.
- W2898024343 title "Radical-Locator Polynomials and Row-Echelon Partial Syndrome Matrices With Applications to Decoding Cyclic Codes" @default.
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- W2898024343 doi "https://doi.org/10.1109/tit.2018.2875546" @default.
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