The weights in MDS codes

The weights in MDS codes

The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses t...

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Bibliographic Details
Main Authors: Ezerman, Martianus Frederic, Grassl, Markus, Sole, Patrick
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2019
Subjects:
DRNTU::Science::Mathematics
Covering Radius
MDS Codes
Online Access:https://hdl.handle.net/10356/100370
http://hdl.handle.net/10220/48554
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Institution: Nanyang Technological University
Language: English
Description
Summary:The weights in maximum distance separable (MDS) codes of length n and dimension k over the finite field GF(q) are studied. Up to some explicit exceptional cases, the MDS codes with parameters given by the MDS conjecture are shown to contain all k weights in the range n - k + 1 to n. The proof uses the covering radius of the dual code.

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