New Constructions of Symbol-Pair Simplex Codes

The symbol-pair simplex codes were introduced by the authors recently, and these codes play a similar role as simplex codes with respect to the Hamming metric. Among other things, the concatenations of the symbol-pair simplex codes are symbol-pair constant-weight codes which are a family of codes achieving the Plotkin-type upper bound of the generalized symbol-pair weight, and thus provide optimal security in the data transmission with the symbol-pair metric in the wire-tap channel with the coset coding scheme. Motivated by the mentioned applications, we present new constructions of symbol-pair simplex codes over any finite field.