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Reports (Research Report) Year : 1999

Generalized Hamming Weight as a Weight Function


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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inria-00072900 , version 1 (24-05-2006)


  • HAL Id : inria-00072900 , version 1


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