TY - CHAP
T1 - Constructions of Nonequivalent Fp-Additive Generalised Hadamard Codes
AU - Dougherty, Steven T.
AU - Rifa, Josep
AU - Villanueva, Merce
N1 - Funding Information:
This work was partially supported by the Spanish MINECO under Grants TIN2016-77918-P and PID2019-104664GB-I00.
Publisher Copyright:
© 2020 IEEE.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/6
Y1 - 2020/6
N2 - A subset of a vector space Fnq is K-additive if it is a linear space over the subfield K C Fq. Let q = pe, p prime, and e > 1. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes which are Fp-additive are established. For specific ranks and dimensions of the kernel within these bounds, Fp-additive GH codes are constructed. Moreover, for the case e = 2, it is shown that the given bounds are tight and it is possible to construct an Fp-additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are selforthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes.
AB - A subset of a vector space Fnq is K-additive if it is a linear space over the subfield K C Fq. Let q = pe, p prime, and e > 1. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes which are Fp-additive are established. For specific ranks and dimensions of the kernel within these bounds, Fp-additive GH codes are constructed. Moreover, for the case e = 2, it is shown that the given bounds are tight and it is possible to construct an Fp-additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are selforthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes.
UR - http://www.scopus.com/inward/record.url?scp=85090410399&partnerID=8YFLogxK
U2 - 10.1109/ISIT44484.2020.9173993
DO - 10.1109/ISIT44484.2020.9173993
M3 - Chapter
AN - SCOPUS:85090410399
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 150
EP - 155
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
ER -