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Computer Science > Information Theory

arXiv:1807.11798 (cs)
[Submitted on 31 Jul 2018 (v1), last revised 3 Apr 2019 (this version, v4)]

Title:A note on full weight spectrum codes

Authors:Tim L. Alderson
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Abstract:A linear $ [n,k]_q $ code $ C $ is said to be a full weight spectrum (FWS) code if there exist codewords of each nonzero weight less than or equal to $ n $. In this brief communication we determine necessary and sufficient conditions for the existence of linear $ [n,k]_q $ full weight spectrum (FWS) codes. Central to our approach is the geometric view of linear codes, whereby columns of a generator matrix correspond to points in $ PG(k-1,q) $.
Subjects: Information Theory (cs.IT); Combinatorics (math.CO)
MSC classes: 94B05, 94B65, 94B25
Cite as: arXiv:1807.11798 [cs.IT]
  (or arXiv:1807.11798v4 [cs.IT] for this version)
  https://doi.org/10.48550/arXiv.1807.11798
Journal reference: Trans. Comb. 8 (2019), no. 3, 15-22
Related DOI: https://doi.org/10.22108/toc.2019.112621.1584

Submission history

From: Tim Alderson [view email]
[v1] Tue, 31 Jul 2018 13:05:20 UTC (10 KB)
[v2] Mon, 20 Aug 2018 18:01:52 UTC (12 KB)
[v3] Thu, 8 Nov 2018 19:17:44 UTC (12 KB)
[v4] Wed, 3 Apr 2019 16:12:24 UTC (11 KB)
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