图上线性码的可观测性、可控性和局部可约性
Observability, Controllability and Local Reducibility of Linear Codes on Graphs
AI总结：
研究有限图上线性码实现的可观测性、可控性与局部可约性之间的关系，证明了不可观测或不可控的实现是局部可约的，并分析了奇偶校验实现和咬尾网格实现的特殊情况。
摘要：
本文关注有限图上线性码实现的局部可约性。修剪性和恰当性是约束码的对偶性质。如果任意约束码不同时满足修剪性和恰当性，则线性实现是局部可约的。在有限无环图上，线性实现是最小的当且仅当每个约束码既是修剪的又是恰当的。线性实现称为可观测的如果它是单射的，称为可控的如果所有约束是独立的。可观测性和可控性是对偶性质。不可观测或不可控的实现是局部可约的。奇偶校验实现是不可控的当且仅当它具有冗余的奇偶校验。咬尾网格实现是不可控的当且仅当其轨迹划分为不连通的子实现。一般的图形实现不具有此性质。
英文摘要：
This paper is concerned with the local reducibility properties of linear realizations of codes on finite graphs. Trimness and properness are dual properties of constraint codes. A linear realization is locally reducible if any constraint code is not both trim and proper. On a finite cycle-free graph, a linear realization is minimal if and only if every constraint code is both trim and proper. A linear realization is called observable if it is one-to-one, and controllable if all constraints are independent. Observability and controllability are dual properties. An unobservable or uncontrollable realization is locally reducible. A parity-check realization is uncontrollable if and only if it has redundant parity checks. A tail-biting trellis realization is uncontrollable if and only if its trajectories partition into disconnected subrealizations. General graphical realizations do not share this property.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
