<p>In this paper, we first study the linear complementary pair (abbreviated to LCP) of codes over finite non-chain rings <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4687_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="223" /> </InlineMediaObject> <EquationSource Format="TEX">$R_{u,v,q}={\mathbb {F}}_q+u{\mathbb {F}}_q+ v{\mathbb {F}}_q+uv{\mathbb {F}}_q$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>R</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> <mo>=</mo> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> <mo>+</mo> <mi>u</mi> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> <mo>+</mo> <mi>v</mi> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> <mo>+</mo> <mi>u</mi> <mi>v</mi> <msub> <mi mathvariant="double-struck">F</mi> <mi>q</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4687_Article_IEq2.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="104" /> </InlineMediaObject> <EquationSource Format="TEX">$u^2=u,v^2=v$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>=</mo> <mi>u</mi> <mo>,</mo> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>=</mo> <mi>v</mi> </mrow> </math></EquationSource> </InlineEquation>. Then we provide a method of constructing entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes from an LCP of codes of length <i>n</i> over <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4687_Article_IEq3.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$R_{u,v,q}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>R</mi> <mrow> <mi>u</mi> <mo>,</mo> <mi>v</mi> <mo>,</mo> <mi>q</mi> </mrow> </msub> </math></EquationSource> </InlineEquation> using CSS. To enrich the variety of available EAQEC codes, some new EAQEC codes are given in the sense that their parameters are different from all the previous constructions.</p>

New EAQEC codes from LCP of codes over finite non-chain rings

期刊论文
发表日期：

2025年2月24日

查看全文

Peng Hu,
Xiusheng Liu

摘要

In this paper, we first study the linear complementary pair (abbreviated to LCP) of codes over finite non-chain rings $R_{u,v,q}={\mathbb {F}}_q+u{\mathbb {F}}_q+ v{\mathbb {F}}_q+uv{\mathbb {F}}_q$ $R_{u, v, q} = F_{q} + u F_{q} + v F_{q} + u v F_{q}$ with $u^2=u,v^2=v$ $u^{2} = u, v^{2} = v$ . Then we provide a method of constructing entanglement-assisted quantum error-correcting (abbreviated to EAQEC) codes from an LCP of codes of length n over $R_{u,v,q}$ $R_{u, v, q}$ using CSS. To enrich the variety of available EAQEC codes, some new EAQEC codes are given in the sense that their parameters are different from all the previous constructions.