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Computing general error locator polynomial of 3-error-correcting BCH codes via syndrome varieties using minimal polynomial
http://hdl.handle.net/2297/48730
http://hdl.handle.net/2297/4873076b81b0f-505a-47b1-b7bf-67753fe1179f
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
ISCS2015Proceedings-80-85.pdf (254.8 kB)
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| Item type | 報告書 / Research Paper(1) | |||||
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| 公開日 | 2017-10-03 | |||||
| タイトル | ||||||
| タイトル | Computing general error locator polynomial of 3-error-correcting BCH codes via syndrome varieties using minimal polynomial | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_18ws | |||||
| 資源タイプ | research report | |||||
| 著者 |
Muhammad, Zaki Almuzakki
× Muhammad, Zaki Almuzakki× Ohara, Katsuyoshi |
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| 書誌情報 |
Recent development in computational science 巻 6, p. 80-85, 発行日 2015-05-31 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 2223-0785 | |||||
| 出版者 | ||||||
| 出版者 | Kanazawa e-Publishing | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | BCH codes are subclass of cyclic codes with strong properties and have been known for years. In 1994, Chen, Reed, Helleseth, and Truong proposed a decoding procedure for t-error-correcting codes via CRHT syndrome variety using computation of lexicographical Gr¨obner bases of the ideal. In 2005, Orsini and Sala added polynomial χl,l˜, 1 ≤ l < l˜≤ t, to a system of algebraic equations I to make sure that the position of any two errors are distinct or at least one of them is zero. In 2014, Takuya Fushisato proposed a modified system J to solve 2-error-correcting BCH codes problem. Here the polynomial τj ∈ J is a divisor of σj and contain all possible syndromes of type 0, αi1 , αi1 + αi2 ∈ Fqm as roots. Generally, τj may be regarded as the minimal polynomial of the roots. In this paper, Fushisato’s system is generalized into K in which Ωj ∈ K contains all possible roots of t-error-correcting BCH codes in the set Sol ⊆ Fqm . Using the system of polyno-mials K, the general error locator polynomials of 3-error-correcting codes could be computed and the computation time of some codes were reduced. | |||||
| 内容記述 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Selected Papers from the International Symposium on Computational Science - International Symposium on Computational Science Kanazawa University, Japan | |||||
| 権利 | ||||||
| 権利情報 | Organizing Committee of ISCS 2015 | |||||
| 著者版フラグ | ||||||
| 出版タイプ | VoR | |||||
| 出版タイプResource | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |||||
