Weight hierarchies of linear codes satisfying the almost chain condition |
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| Authors: | Email author" target="_blank">Chen?Wende?Email author Torleiv?Kl?ve |
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| Affiliation: | 1. Laboratory of Systems and Control, Information Security Center, Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China;
2. Department of Informatics, University of Bergen, Bergen High Technology Center, N-5020 Bergen, Norway |
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| Abstract: | The weight hierarchy of a linear n, k; q] code C over GF(q) is the sequence (d1, d2,…,dk) where dr is the size of the smallest support of an r-dimensional subcode of C. An n, k; q] codehas dimension r and support of size dr for all r. Further, C satisfies the almost chain condition ifit does not satisfy the chain condition, but there exist subcodes Dr of dimension r and support offor a sequence to be the weight hierarchy of a code satisfying the almost chain condition is given.Further, explicit constructions of such codes are given, showing that in almost all cases, the necessaryconditions are also sufficient. |
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| Keywords: | weight hierarchy linear code almost chain condition |
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