new code upper bounds for the folded n cube

• DOI: 10.48550/arxiv.1801.06971
• Publication Date: 2020-05-01
• Authors: Lihang Hou; Wei-Hsuan Yu; Bo Hou; Suogang Gao
• Keywords: FOS: Mathematics; Mathematics - Combinatorics; 0102 computer and information sciences; Combinatorics (math.CO); 0101 mathematics; 01 natural sciences

Let $��$ denote a distance-regular graph. The maximum size of codewords with minimum distance at least $d$ is denoted by $A(��,d)$. Let $\square_n$ denote the folded $n$-cube $H(n,2)$. We give an upper bound on $A(\square_n,d)$ based on block-diagonalizing the Terwilliger algebra of $\square_n$ and on semidefinite programming.The technique of this paper is an extension of the approach taken by A. Schrijver \cite{s} on the study of $A(H(n,2),d)$.