Abstract
In this work we study a weak order ideal associated with the coset leaders of a non-binary linear code. This set allows the incrementally computation of the coset leaders and the definitions of the set of leader codewords. This set of codewords has some nice properties related to the monotonicity of the weight compatible order on the generalized support of a vector in \(\mathbb {F}_q^n\) which allows to describe a test set, a trial set and the set of zero neighbours of a linear code in terms of the leader codewords.
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Mijail Borges-Quintana has been partially supported by a post-doctorate scholarship at the University of Valladolid (09-2014 to 02-2015) by Erasmus Mundus Program, Mundus Lindo Project.
Edgar Martínez-Moro has been partially supported by the Spanish MINECO under Grants MTM2015-65764-C3-1-P and MTM2015-69138-REDT.
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Borges-Quintana, M., Borges-Trenard, M.Á. & Martínez-Moro, E. On the Weak Order Ideal Associated to Linear Codes. Math.Comput.Sci. 12, 339–347 (2018). https://doi.org/10.1007/s11786-018-0349-1
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DOI: https://doi.org/10.1007/s11786-018-0349-1