2017/09/07 by Josep Rifà, Rifà, J., Emilio Suárez-Canedo +1
Computer Science · Engineering · Mathematics · #5B #5E #94B #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · doi:10.48550/arxiv.1709.02465
openalex publication_date 2017/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
Hadamard full propelinear codes (HFP-codes) are introduced and their equivalence with Hadamard groups is proven (on the other hand, it is already known the equivalence of Hadamard groups with relative (4n,2,4n,2n)-difference sets in a group and also with cocyclic Hadamard matrices). We compute the available values for the rank and dimension of the kernel of HFP-codes of type Q and we show that the dimension of the kernel is always 1 or 2. We also show that when the dimension of the kernel is 2 then the dimension of the kernel of the transposed code is 1 (so, both codes are not equivalent). Finally, we give a construction method such that from an HFP-code of length 4n, dimension of the kernel k=2, and maximum rank r=2n, we obtain an HFP-code of double length 8n, dimension of the kernel k=2, and maximum rank r=4n.