In this note, we apply some techniques developed in [1]-[3] to give a particular construction of bivariate Abelian Codes from cyclic codes, multiplying their dimension and preserving their apparent distance. We show that, in the case of cyclic codes whose maximum BCH bound equals its minimum distance the obtained abelian code verifies the same property; that is, the strong apparent distance and the minimum distance coincide. We finally use this construction to multiply Reed-Solomon codes to abelian codes

翻译：本文应用文献[1]-[3]中发展的技术，从循环码出发给出双变量阿贝尔码的一种特定构造方法，该方法在保持表观距离不变的同时将循环码的维数相乘。我们证明，对于最大BCH界等于最小距离的循环码，所得到的阿贝尔码具有相同性质，即强表观距离与最小距离相等。最后，我们利用此构造将Reed-Solomon码扩展为阿贝尔码。