Switching of covering codes.

Switching is a local transformation of a combinatorial structure that does not alter the main parameters. Switching of binary covering codes is studied here. In particular, the well-known transformation of error-correcting codes by adding a parity-check bit and deleting one coordinate is applied to covering codes. Such a transformation is termed a semiflip, and finite products of semiflips are semiautomorphisms. It is shown that for each code length n ≥ 3 , the semiautomorphisms are exactly the bijections that preserve the set of r -balls for each radius r . Switching of optimal codes of size at most 7 and of codes attaining K ( 8 , 1 ) = 32 is further investigated, and semiautomorphism classes of these codes are found. The paper ends with an application of semiautomorphisms to the theory of normality of covering codes. [ABSTRACT FROM AUTHOR]