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Generalized Hamming Weight as a Weight Function

Dmitrii Yu Nogin 1
1 CODES - Coding and cryptography
Inria Paris-Rocquencourt
Abstract : 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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https://hal.inria.fr/inria-00072900
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Submitted on : Wednesday, May 24, 2006 - 11:14:22 AM
Last modification on : Friday, February 4, 2022 - 3:10:23 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:27:08 PM

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  • HAL Id : inria-00072900, version 1

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Dmitrii Yu Nogin. Generalized Hamming Weight as a Weight Function. [Research Report] RR-3762, INRIA. 1999. ⟨inria-00072900⟩

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