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<p>In this work the construction of LRC codes given in Chara et al. (Finite Fields Appl 94:102359, 2024) is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(n \approx q^4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mo>≈</mo> <msup> <mi>q</mi> <mn>4</mn> </msup> </mrow> </math></EquationSource> </InlineEquation>, dimension and distance of order <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>q</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation>, and locality <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(r =q-1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>r</mi> <mo>=</mo> <mi>q</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. In addition, the cases <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(q = 4\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>4</mn> </mrow> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(q=8\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>q</mi> <mo>=</mo> <mn>8</mn> </mrow> </math></EquationSource> </InlineEquation> are studied.</p>

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LRC codes over characteristic 2

  • 期刊论文

  • 发表日期：

    2026年4月9日

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  • F. Galluccio

摘要

In this work the construction of LRC codes given in Chara et al. (Finite Fields Appl 94:102359, 2024) is completed, in the case of even characteristic. A general construction is presented, that enables us to obtain linear LRC codes of large length \(n \approx q^4\) n ≈ q 4 , dimension and distance of order \(q^4\) q 4 , and locality \(r =q-1\) r = q - 1 . In addition, the cases \(q = 4\) q = 4 and \(q=8\) q = 8 are studied.