On shortening construction of self-orthogonal quaternary codes

For a given quaternary self-orthogonal (SO) code, using information of weights of codewords in the dual of the binary code generated by the supports of this SO code, one can construct new quaternary SO code by shortening method. Two methods of determining weights of codewords in the dual of the binary support code of a given large length SO code are presented. Using these methods, we construct many SO codes from a quantum 286-cap in PG(6, 4), and deduce existence of many quantum caps in PG(6, 4) and good quantum codes of distance 4.