TY - JOUR
T1 - On the intersection of ℤ2ℤ4-Additive perfect codes
AU - Rifà, Josep
AU - Solov'eva, Faina Ivanovna
AU - Villanueva, Mercè
N1 - Funding Information:
Manuscript received December 2, 2006; revised May 28, 2007. This work has been partially supported by the Spanish MEC and the European FEDER Grant MTM2006-03250 and also by the UAB Grant PNL2006-13. Part of this manuscript was produced during a visit by F. I. Solov’eva to the Autonomous University of Barcelona under the Grant VIS2007-16. The material in this correspondence was presented in part at the International Workshop on Coding and Cryptography (WCC’07), Versailles, France, April 2007.
PY - 2008/3
Y1 - 2008/3
N2 - The intersection problem for ℤ2ℤ4 -additive (extended and nonextended) perfect codes, i.e., which are the possibilities for the number of codewords in the intersection of two ℤ2ℤ4-additive codes C1 and C2 of the same length, is investigated. Lower and upper bounds for the intersection number are computed and, for any value between these bounds, codes which have this given intersection value are constructed. For all these ℤ2ℤ4-additive codes C1 and C2, the abelian group structure of the intersection codes C1 ∩ C2 is characterized. The parameters of this abelian group structure corresponding to the intersection codes are computed and lower and upper bounds for these parameters are established. Finally, for all possible parameters between these bounds, constructions of codes with these parameters for their intersections are given.
AB - The intersection problem for ℤ2ℤ4 -additive (extended and nonextended) perfect codes, i.e., which are the possibilities for the number of codewords in the intersection of two ℤ2ℤ4-additive codes C1 and C2 of the same length, is investigated. Lower and upper bounds for the intersection number are computed and, for any value between these bounds, codes which have this given intersection value are constructed. For all these ℤ2ℤ4-additive codes C1 and C2, the abelian group structure of the intersection codes C1 ∩ C2 is characterized. The parameters of this abelian group structure corresponding to the intersection codes are computed and lower and upper bounds for these parameters are established. Finally, for all possible parameters between these bounds, constructions of codes with these parameters for their intersections are given.
KW - Additive codes
KW - Extended perfect codes
KW - Intersection
KW - Perfect codes
UR - https://www.scopus.com/pages/publications/40949119917
U2 - 10.1109/TIT.2007.915917
DO - 10.1109/TIT.2007.915917
M3 - Article
AN - SCOPUS:40949119917
SN - 0018-9448
VL - 54
SP - 1346
EP - 1356
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 3
ER -