TY - JOUR
T1 - A characterization of Z2Z2[u]-linear codes
AU - Borges, Joaquim
AU - Fernández-Córdoba, Cristina
PY - 2018/7/1
Y1 - 2018/7/1
N2 - © 2017, Springer Science+Business Media, LLC. We prove that the class of Z2Z2[ u] -linear codes is exactly the class of Z2-linear codes with automorphism group of even order. Using this characterization, we give examples of known codes, e.g. perfect codes, which have a nontrivial Z2Z2[ u] structure. Moreover, we exhibit some examples of Z2-linear codes which are not Z2Z2[ u] -linear. Also, we state that the duality of Z2Z2[ u] -linear codes is the same as the duality of Z2-linear codes. Finally, we prove that the class of Z2Z4-linear codes which are also Z2-linear is strictly contained in the class of Z2Z2[ u] -linear codes.
AB - © 2017, Springer Science+Business Media, LLC. We prove that the class of Z2Z2[ u] -linear codes is exactly the class of Z2-linear codes with automorphism group of even order. Using this characterization, we give examples of known codes, e.g. perfect codes, which have a nontrivial Z2Z2[ u] structure. Moreover, we exhibit some examples of Z2-linear codes which are not Z2Z2[ u] -linear. Also, we state that the duality of Z2Z2[ u] -linear codes is the same as the duality of Z2-linear codes. Finally, we prove that the class of Z2Z4-linear codes which are also Z2-linear is strictly contained in the class of Z2Z2[ u] -linear codes.
KW - Z -linear codes 2
KW - Z Z -linear codes 2 4
KW - Z Z [ u] -linear codes 2 2
U2 - 10.1007/s10623-017-0401-1
DO - 10.1007/s10623-017-0401-1
M3 - Article
SN - 0925-1022
VL - 86
SP - 1377
EP - 1389
JO - Designs, Codes, and Cryptography
JF - Designs, Codes, and Cryptography
IS - 7
ER -