Weight Functions and Generalized Hamming Weights of Linear Codes

Weight Functions and Generalized Hamming Weights of Linear Codes We prove that the weight function wt: $$\mathbb{F}_q^k \to \mathbb{Z}$$ on a set of messages uniquely determines a linear code of dimension k up to equivalence. We propose a natural way to extend the rth generalized Hamming weight, that is, a function on r-subspaces of a code C, to a function on $$\mathbb{F}_q^{\left( {_r^k } \right)} \cong \Lambda ^r C$$ . Using this, we show that, for each linear code C and any integer r ≤ k = dim C, a linear code exists whose weight distribution corresponds to a part of the generalized weight spectrum of C, from the rth weights to the kth. In particular, the minimum distance of this code is proportional to the rth generalized weight of C. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Weight Functions and Generalized Hamming Weights of Linear Codes

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Copyright © 2005 by MAIK “Nauka/Interperiodica”
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
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