TY - JOUR
T1 - Constructions of Abelian Codes Multiplying Dimension of Cyclic Codes
AU - Bernal, José Joaquín
AU - Bueno-Carreño, Diana H.
AU - Simón, Juan Jacobo
N1 - Publisher Copyright:
© 2019, Springer Nature Switzerland AG.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - 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.
AB - 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.
KW - Abelian codes
KW - Apparent distance
KW - Cyclic codes
UR - http://www.scopus.com/inward/record.url?scp=85084367885&partnerID=8YFLogxK
U2 - 10.1007/s11786-019-00416-5
DO - 10.1007/s11786-019-00416-5
M3 - Article
AN - SCOPUS:85084367885
SN - 1661-8270
VL - 14
SP - 415
EP - 421
JO - Mathematics in Computer Science
JF - Mathematics in Computer Science
IS - 2
ER -