Asymptotic results on codes for symmetric, unidirectional, and asymmetric error control

The asymptotic behavior of the rates of optimal codes correcting and/or detecting combinations of symmetric, unidirectional, and/or asymmetric errors is studied. These rates are expressed in terms of the rate of optimal codes,,with a certain Hamming distance. As a consequence, well-known bounds on the latter rate can also be applied to bound the former rates. Furthermore, it turns out that, without losing rate asymptotically, any error control combination can be upgraded to simultaneous symmetric error correction/detection and all unidirectional error detection