Constructions of Abelian Codes Multiplying Dimension of Cyclic Codes

In this note, we apply some techniques developed in Bernal et al. (IEEE Trans Inf Theory 62(2):655–668, 2016; Adv Math Commun 10:459–474, 2016; IEEE Trans Inf Theory 2018. https://doi.org/10.1109/TIT.2018.2868446) 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.