Lower bounds on the minimum distance of long codes in the Lee metric

Hugues Randriam; Lin Sok; Patrick Solé

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arXiv · 1302.2246

Lower bounds on the minimum distance of long codes in the Lee metric

Hugues Randriam·Lin Sok·Patrick Solé

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Abstract

The Gilbert type bound for codes in the title is reviewed, both for small and large alphabets. Constructive lower bounds better than these existential bounds are derived from geometric codes, either over Fp or Fp2 ; or over even degree extensions of Fp: In the latter case the approach is concatena- tion with a good code for the Hamming metric as outer code and a short code for the Lee metric as an inner code. In the former case lower bounds on the minimum Lee distance are derived by algebraic geometric arguments inspired by results of Wu, Kuijper, Udaya (2007).

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Hugues Randriam, Lin Sok, Patrick Solé. 2013-02-09. Lower bounds on the minimum distance of long codes in the Lee metric. https://arxiv.org/abs/1302.2246

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