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<p>The negcyclic codes extend the algebraic structure of cyclic codes, providing a key tool for building quantum error-correcting codes and efficiently addressing symmetric channels. This paper is devoted to the study of negacyclic dually-BCH codes over <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb{F}_q\)</EquationSource> </InlineEquation> having length <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(n=\frac{q^m-1}{2(q-1)}\)</EquationSource> </InlineEquation>. The largest odd coset leaders modulo <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(2n\)</EquationSource> </InlineEquation> are derived for several cases, and the necessary and sufficient conditions are obtained for a negacyclic BCH code of length <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(n\)</EquationSource> </InlineEquation> over <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\mathbb{F}_q\)</EquationSource> </InlineEquation> to be negacyclic dually-BCH.</p>

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Negacyclic dually-BCH codes of length \(\frac{q^m-1}{2(q-1)}\)

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Binbin Pang,
  • Yuanhao Lin,
  • Haifeng Yu

摘要

The negcyclic codes extend the algebraic structure of cyclic codes, providing a key tool for building quantum error-correcting codes and efficiently addressing symmetric channels. This paper is devoted to the study of negacyclic dually-BCH codes over \(\mathbb{F}_q\) having length \(n=\frac{q^m-1}{2(q-1)}\) . The largest odd coset leaders modulo \(2n\) are derived for several cases, and the necessary and sufficient conditions are obtained for a negacyclic BCH code of length \(n\) over \(\mathbb{F}_q\) to be negacyclic dually-BCH.