2020 IEEE International Symposium
on Information Theory
21-26 June 2020 • Los Angeles, California, USA
| Paper ID | A.5.4 | ||
| Paper Title | Constructions of Nonequivalent Fp-Additive Generalised Hadamard Codes | ||
| Authors | Steven T. Dougherty, University of Scranton, United States; Josep Rifà, Mercè Villanueva, Universitat Autònoma de Barcelona, Spain | ||
| Session | A.5: Combinatorial Coding Theory II | ||
| Presentation | Lecture | ||
| Track | Algebraic and Combinatorial Coding Theory | ||
| Manuscript | Click here to download the manuscript | ||
| Virtual Presentation | Click here to watch in the Virtual Symposium | ||
| Abstract | A subset of a vector space of dimension n over a finite field GF(q) is K-additive if it is a linear space over the subfield K of GF(q). Let q be equal to a prime p to e-th power with e>1. Bounds on the rank and dimension of the kernel of generalised Hadamard (GH) codes which are GF(p)-additive are established. For specific ranks and dimensions of the kernel within these bounds, GF(p)-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 GF(p)-additive GH code for all allowable ranks and dimensions of the kernel between these bounds. Finally, we also prove that these codes are self-orthogonal with respect to the trace Hermitian inner product, and generate pure quantum codes. | ||
Plan Ahead
2021 IEEE International Symposium on Information Theory
11-16 July 2021 | Melbourne, Victoria, Australia
