The Berlekamp-Massey Algorithm and the Euclidean Algorithm: a Closer Link

Reverse Berlekamp-Massey Decoding

We propose a new algorithm for decoding Reed-Solomon codes (up to half the minimum distance) and for computing inverses in $F[x]/m(x)$. The proposed algorithm is similar in spirit and structure to the Berlekamp-Massey algorithm, but it works naturally for general $m(x)$.

Berlekamp-Massey-Sakata算法实现中未知校正子值的推断

Inference of unknown syndrome values in the implementation of the Berlekamp-Massey-Sakata algorithm

本文研究在代数几何码中实现Berlekamp-Massey-Sakata算法时缺失校正子值的推断问题，并将其结果用于解决阿贝尔码的校正子校正。

Berlekamp-Massey-Sakata算法的新方法：改进定位子译码

A new approach to the Berlekamp-Massey-Sakata Algorithm. Improving Locator Decoding

本文通过确定保证BMS算法最终输出为线性递归关系理想Gröbner基的指标条件，提出改进abelian码定位子译码的新方法。

The Berlekamp-Massey Algorithm via Minimal Polynomials

We present a recursive minimal polynomial theorem for finite sequences over a commutative integral domain $D$. This theorem is relative to any element of $D$. The ingredients are: the arithmetic of Laurent polynomials over $D$, a recursive 'index function' and simple mathematical induction. Taking reciprocals gives a 'Berlekamp-Massey theorem' i.e. a recursive construction of the polynomials arising in the Berlekamp-Massey algorithm, relative to any element of $D$. The recursive theorem readily yields the iterative minimal polynomial algorithm due to the author and a transparent derivation of …

Inverse-free Berlekamp-Massey-Sakata Algorithm and Small Decoders for Algebraic-Geometric Codes

This paper proposes a novel algorithm for finding error-locators of algebraic-geometric codes that can eliminate the division-calculations of finite fields from the Berlekamp-Massey-Sakata algorithm. This inverse-free algorithm provides full performance in correcting a certain class of errors, generic errors, which includes most errors, and can decode codes on algebraic curves without the determination of unknown syndromes. Moreover, we propose three different kinds of architectures that our algorithm can be applied to, and we represent the control operation of shift-registers and switches at …

不完整表格中的双曲集合

Hyperbolic Sets in Incomplete Tables

本文将Berlekamp-Massey-Sakata算法的实现结果推广到含有未知值的不完整数据表上，研究其中的双曲集合。