Q-codes
A new family of cyclic codes over GF(4), the so-called Q-codes, are introduced. They are defined analogously to binary, dyadic codes in terms of their idempotents. All self-dual and strictly self-dual extended cyclic codes are extended Q-codes. Especially the Quadratic Residue codes are contained in the definition of Q-codes. Properties of Q-codes, e.g. the minimum weight vectors and a square root bound, are investigated. These results are used to obtain partially a new proof for the non- existence of cyclic projective planes of certain even orders n. Finally a table of Q-codes of all prime lengths until 41 and composite lengths until 25 is given.
scientific article; zbMATH DE number 4114552
scientific article