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<p>Due to their efficient decoding algorithms, convolutional codes are crucial in a wide range of applications. In this paper, by combining the deformation of the Vandermonde matrix, we construct some new families of convolutional codes with memory 1 and maximum distance profile. The required field size for our construction is <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(O(n^{k-1})\)</EquationSource> </InlineEquation> for <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(k=2,3\)</EquationSource> </InlineEquation>. This improves the known construction of convolutional codes with memory 1 and maximum distance profile.</p>

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New constructions of MDP convolutional codes with memory 1 for \(\varvec{k=2,3}\)

  • 期刊论文

  • 发表日期：

    2026年2月7日

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  • Zhiqiang Cheng

摘要

Due to their efficient decoding algorithms, convolutional codes are crucial in a wide range of applications. In this paper, by combining the deformation of the Vandermonde matrix, we construct some new families of convolutional codes with memory 1 and maximum distance profile. The required field size for our construction is \(O(n^{k-1})\) for \(k=2,3\) . This improves the known construction of convolutional codes with memory 1 and maximum distance profile.