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Relative generalized hamming weights and extended weight polynomials of almost affine codes

Permanent link
https://hdl.handle.net/10037/12402
DOI
https://doi.org/10.1007/978-3-319-66278-7_17
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Accepted manuscript version (PDF)
Date
2017-08-23
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Johnsen, Trygve; Verdure, Hugues
Abstract
This paper is devoted to giving a generalization from linear codes to the larger class of almost affine codes of two different results. One such result is how one can express the relative generalized Hamming weights of a pair of codes in terms of intersection properties between the smallest of these codes and subcodes of the largest code. The other result tells how one can find the extended weight polynomials, expressing the number of codewords of each possible weight, for each code in an infinite hierarchy of extensions of a code over a given alphabet. Our tools will be demi-matroids and matroids.
Description
This is a post-peer-review, pre-copyedit version of an article published in Lecture Notes in Computer Science, International Castle Meeting on Coding Theory and Applications ICMCTA 2017: Coding Theory and Applications, 207-216. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-66278-7_17 .
Publisher
Springer
Citation
Johnsen, T., Verdure, H.. (2017) Relative generalized hamming weights and extended weight polynomials of almost affine codes. Lecture Notes in Computer Science. 10495 LNCS:207-216
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