论文标题
不可循环代码和相关后果的B符号重量分布
The b-symbol weight distribution of irreducible cyclic codes and related consequences
论文作者
论文摘要
$ b $ -Symbol读取通道是由于高密度数据存储系统中阅读过程的局限性而激发的。相应的新指标是称为$ b $ -Symbol重量度量的锤式度量的概括，并已成为编码理论的重要对象。在本文中，通过使用高斯时期和一个新的不变$ \＃u（b，j，n_1）$，介绍了不可约循环代码的一般$ b $ -Symbol重量枚举公式。相关的$ b $ -Symbol重量层次结构$ \ {d_1（\ c），d_2（\ c），\ ldots，d_k（\ c）\} $（$ k = \ dim（\ c）$）在某些情况下给出。给出了某些类别不可约的循环代码中最佳的缩短代码，其中缩短集合$ \ MATHCAL {T} $是$ B $ -Symbol的互补集，其中某些代码字支持具有最小的$ b $ -symbol重量。
The $b$-symbol read channel is motivated by the limitations of the reading process in high density data storage systems. The corresponding new metric is a generalization of the Hamming metric known as the $b$-symbol weight metric and has become an important object in coding theory. In this paper, the general $b$-symbol weight enumerator formula for irreducible cyclic codes is presented by using the Gaussian period and a new invariant $\#U(b,j,N_1)$. The related $b$-symbol weight hierarchies $\{d_1(\C),d_2(\C),\ldots,d_K(\C)\}$ ($K=\dim(\C)$) are given for some cases. The shortened codes which are optimal from some classes of irreducible cyclic codes are given, where the shorten set $\mathcal{T}$ is the complementary set of $b$-symbol support of some codeword with the minimal $b$-symbol weight.
