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Weight Distributions of Two Classes of Optimal <span class="MathJax_Preview" style="">(r, \delta)</span><script type="math/tex" id="MathJax-Element-1">(r, \delta)</script>-Locally Repairable Codes | IEEE Conference Publication | IEEE Xplore

Weight Distributions of Two Classes of Optimal (r, \delta)-Locally Repairable Codes


Abstract:

An (r,\ \delta) -locally repairable code (LRC) is an [n,\ k,\ d] linear code that permits the reconstruction of each code symbol by accessing up to r other symbols ...Show More

Abstract:

An (r,\ \delta) -locally repairable code (LRC) is an [n,\ k,\ d] linear code that permits the reconstruction of each code symbol by accessing up to r other symbols in the event of at most \delta-1 erasures. In this paper, by characterizing the weight type hierarchy of codewords, we offer explicit expressions of the weight distributions for q-ary optimal (r=2,\ \delta) -LRCs with minimum distance 2\delta+1 and even code dimension, as well as for (r,\ \delta) -LRCs with minimum distance \delta+1 under the condition that k\geq 5r-1. These corresponding parameter conditions ensure all the (r,\ \delta) -LRCs we studied possess disjoint locality groups. Furthermore, we demonstrate that the weight distributions of optimal (r=2,\ \delta) -LRCs can be uniquely determined only for specific minimum distances of \delta, \delta+1 or 2\delta+1.
Date of Conference: 24-28 November 2024
Date Added to IEEE Xplore: 30 December 2024
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Conference Location: Shenzhen, China

References

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