Quantum bivariate bicycle codes with weight-8 checks surpassing the BB benchmark
研究通过开发具有8权重检查的双变量自行车码,使用精确验证的搜索管道构建和认证新码,超越了BB基准。
研究通过开发具有8权重检查的双变量自行车码,使用精确验证的搜索管道构建和认证新码,超越了BB基准。
本文介绍BVR Sim,一个用于异构空战强化学习的开源环境,通过提供多种飞机模型、统一战术动作接口等方法解决长时决策和能量管理等问题。
研究通过小域上的负循环码和重复根循环码构建量子局部可恢复码,解决大字母表需求问题,提出纯度标准及无限家族的纯qLRCs。
This work addresses the challenge of efficiently determining the dimension and distance of quantum Bicycle LDPC codes, which traditionally rely on group-algebraic constructions that hinder the discovery of high-performance short codes. The authors reformulate the construction of cyclic Bicycle codes as a purely algebraic problem in the polynomial ring $\mathbb{F}_2[x]/(x^\ell - 1)$. Exploiting the fact that self-orthogonality is automatically satisfied, they show that the code dimension is directly given by a polynomial greatest common divisor, while the distance can be precisely verified via the Calderbank correspondence mapping to additive codes over $\mathbb{F}_4$. This enables efficient pre-screening and systematic enumeration, bypassing group-theoretic limitations. For the first time, an exhaustive algebraic search of Bicycle codes becomes feasible, revealing the onset boundary of the co-set phenomenon and yielding new high-performance codes such as $[[66,20,7]]_2$ ($kd^2/n=14.85$) and $[[46,2,8]]_2$. A complete census at $n=48$ disproves the existence of a $[[48,10,5]]_2$ code, thereby clarifying fundamental construction limits.
This work addresses the limitation in traditional constructions of quantum stabilizer codes, which require classical codes to satisfy Hermitian self-orthogonality. To overcome this constraint, the authors introduce the novel notion of “$r$-nearly self-orthogonal” codes. Starting from an arbitrary classical linear code, they explicitly construct self-orthogonal codes by leveraging Jordan canonical form decomposition, analysis of Hermitian dual spaces, and rank-one perturbation techniques. They further establish a sufficient criterion that guarantees preservation of the minimum distance. The resulting $q$-ary quantum codes achieve parameters $[[n+r, 2k-n+r, \geq d]]_q$, with several concrete instances either surpassing or complementing the best-known codes listed in Grassl’s table.
研究通过开发具有8权重检查的双变量自行车码,使用精确验证的搜索管道构建和认证新码,超越了BB基准。
本文介绍BVR Sim,一个用于异构空战强化学习的开源环境,通过提供多种飞机模型、统一战术动作接口等方法解决长时决策和能量管理等问题。
研究通过小域上的负循环码和重复根循环码构建量子局部可恢复码,解决大字母表需求问题,提出纯度标准及无限家族的纯qLRCs。
This work addresses the challenge of efficiently determining the dimension and distance of quantum Bicycle LDPC codes, which traditionally rely on group-algebraic constructions that hinder the discovery of high-performance short codes. The authors reformulate the construction of cyclic Bicycle codes as a purely algebraic problem in the polynomial ring $\mathbb{F}_2[x]/(x^\ell - 1)$. Exploiting the fact that self-orthogonality is automatically satisfied, they show that the code dimension is directly given by a polynomial greatest common divisor, while the distance can be precisely verified via the Calderbank correspondence mapping to additive codes over $\mathbb{F}_4$. This enables efficient pre-screening and systematic enumeration, bypassing group-theoretic limitations. For the first time, an exhaustive algebraic search of Bicycle codes becomes feasible, revealing the onset boundary of the co-set phenomenon and yielding new high-performance codes such as $[[66,20,7]]_2$ ($kd^2/n=14.85$) and $[[46,2,8]]_2$. A complete census at $n=48$ disproves the existence of a $[[48,10,5]]_2$ code, thereby clarifying fundamental construction limits.
This work addresses the limitation in traditional constructions of quantum stabilizer codes, which require classical codes to satisfy Hermitian self-orthogonality. To overcome this constraint, the authors introduce the novel notion of “$r$-nearly self-orthogonal” codes. Starting from an arbitrary classical linear code, they explicitly construct self-orthogonal codes by leveraging Jordan canonical form decomposition, analysis of Hermitian dual spaces, and rank-one perturbation techniques. They further establish a sufficient criterion that guarantees preservation of the minimum distance. The resulting $q$-ary quantum codes achieve parameters $[[n+r, 2k-n+r, \geq d]]_q$, with several concrete instances either surpassing or complementing the best-known codes listed in Grassl’s table.