论文标题
GRS代码和EGRS代码的等效性
The equivalence of GRS codes and EGRS codes
论文作者
论文摘要
广义的芦苇溶解和扩展广义的芦苇 - 溶解（缩写为GRS和EGRS）是最著名的MDS代码家族，在编码理论和实践中具有广泛的应用。令$ \ mathbb {f} _q $为$ q $元素有限字段，其中$ q $是prime的力量。对于线性代码$ \ MATHCAL {C} $上的$ \ Mathbb {f} _Q $，长度为$ 2 \ le n \ le q $，我们证明$ \ mathcal {c} $是grs代码，并且仅当$ \ m natercal {c} $是egrs code。
Generalized Reed-Solomon and extended generalized Reed-Solomon (abbreviation to GRS and EGRS) codes are the most well-known family of MDS codes with wide applications in coding theory and practice. Let $\mathbb{F}_q$ be the $q$ elements finite field, where $q$ is the power of a prime. For a linear code $\mathcal{C}$ over $\mathbb{F}_q$ with length $2\le n\le q$, we prove that $\mathcal{C}$ is a GRS code if and only if $\mathcal{C}$ is a EGRS code.
