2023/02/23 by Gyanendra K. Verma, Verma, Gyanendra K., R. K. Sharma +1 · 2 citations
Computer Science · Social Sciences · #Coding theory and cryptography #Cooperative Communication and Network Coding #FOS: Computer and information sciences #Information Theory (cs.IT) #Islamic Finance and Communication
paper · pdf · doi:10.48550/arxiv.2302.11791
openalex publication_date 2023/02/23 · openalex created_date 2023/02/25 · openalex updated_date 2026/08/02
In this work, we investigate additive complementary dual (ACD) codes and their construction over finite fields \mathbbFq2 with respect to the trace inner products, where q is a prime power. First, we associate an additive code with a matrix known as a generator matrix. After that, we describe ACD codes in terms of generator matrices for the trace Hermitian and the trace Euclidean inner products. We also construct ACD codes over \mathbbFq2 from linear codes over \mathbbFq. Additionally, we present techniques for constructing ACD codes with various parameters from a given ACD code over \mathbbFq2. By applying these methods, we construct numbers of trace Euclidean and trace Hermitian ACD codes that exhibit better parameters compared to the best known linear codes over \mathbbF9 and \mathbbF4 of the same size and length.