TY - JOUR
T1 - On hadamard full propelinear codes with associated group C2t × C2
AU - Bailera, Ivan
AU - Borges, Joaquim
AU - Rifà, Josep
N1 - Funding Information:
2020 Mathematics Subject Classification: Primary: 5B, 5E, 94B. Key words and phrases: Hadamard full propelinear codes, Hadamard matrices, kernel, rank. This work has been partially supported by the Spanish grant TIN2016-77918-P (AEI/FEDER, UE). ∗ Corresponding author: [email protected].
Publisher Copyright:
© 2021, American Institute of Mathematical Sciences. All rights reserved.
Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/2
Y1 - 2021/2
N2 - We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.
AB - We introduce the Hadamard full propelinear codes that factorize as direct product of groups such that their associated group is C2t × C2. We study the rank, the dimension of the kernel, and the structure of these codes. For several specific parameters we establish some links from circulant Hada-mard matrices and the nonexistence of the codes we study. We prove that the dimension of the kernel of these codes is bounded by 3 if the code is nonlinear. We also get an equivalence between circulant complex Hadamard matrix and a type of Hadamard full propelinear code, and we find a new example of circulant complex Hadamard matrix of order 16.
KW - Hadamard full propelinear codes
KW - Hadamard matrices
KW - Kernel
KW - Rank
UR - http://www.scopus.com/inward/record.url?scp=85099296095&partnerID=8YFLogxK
U2 - 10.3934/amc.2020041
DO - 10.3934/amc.2020041
M3 - Article
AN - SCOPUS:85099296095
SN - 1930-5346
VL - 15
SP - 35
EP - 54
JO - Advances in Mathematics of Communications
JF - Advances in Mathematics of Communications
IS - 1
M1 - 1
ER -