|Constructions of Nonequivalent Fp-Additive Generalised Hadamard Codes
|Steven T. Dougherty, University of Scranton, United States; Josep Rifà, Mercè Villanueva, Universitat Autònoma de Barcelona, Spain
|A.5: Combinatorial Coding Theory II
|Algebraic and Combinatorial Coding Theory
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|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.