Generalized Hamming Weight as a Weight Function
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| Název: | Generalized Hamming Weight as a Weight Function |
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| Autoři: | Nogin, Dmitrii Yu |
| Přispěvatelé: | Coding and cryptography (CODES), Inria Paris-Rocquencourt, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA |
| Zdroj: | https://hal.inria.fr/inria-00072900 ; [Research Report] RR-3762, INRIA. 1999. |
| Informace o vydavateli: | HAL CCSD |
| Rok vydání: | 1999 |
| Sbírka: | Archive ouverte HAL (Hyper Article en Ligne, CCSD - Centre pour la Communication Scientifique Directe) |
| Témata: | GENERALIZED SPECTRUM, GENERALIZED HAMMING WEIGHT, WEIGHT ENUMERATOR, CODE, EQUIVALENCE, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH] |
| Popis: | We prove that the weight function of a linear code, that is, an integer function defined on the vector space of messages, uniquely determines the code up to equivalence. We propose a natural way to extend the r-th generalized Hamming weight, that is, a function on r-subspaces of a code, to a function on the r-th exterior power of the code. Using this, we show that for any linear code C and any integer r not greater than the dimension of C, another code C' exists whose weight distribution corresponds to a part of the generalized weight spectrum of C from the r-th weights to the k-th. In particular, the minimum distance of C' is proportional to the r-th generalized weight of C. |
| Druh dokumentu: | report |
| Jazyk: | English |
| Relation: | Report N°: RR-3762; inria-00072900; https://hal.inria.fr/inria-00072900; https://hal.inria.fr/inria-00072900/document; https://hal.inria.fr/inria-00072900/file/RR-3762.pdf |
| Dostupnost: | https://hal.inria.fr/inria-00072900 https://hal.inria.fr/inria-00072900/document https://hal.inria.fr/inria-00072900/file/RR-3762.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| Přístupové číslo: | edsbas.BACB8B2D |
| Databáze: | BASE |
Nájsť tento článok vo Web of Science | Abstrakt: | We prove that the weight function of a linear code, that is, an integer function defined on the vector space of messages, uniquely determines the code up to equivalence. We propose a natural way to extend the r-th generalized Hamming weight, that is, a function on r-subspaces of a code, to a function on the r-th exterior power of the code. Using this, we show that for any linear code C and any integer r not greater than the dimension of C, another code C' exists whose weight distribution corresponds to a part of the generalized weight spectrum of C from the r-th weights to the k-th. In particular, the minimum distance of C' is proportional to the r-th generalized weight of C. |
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