This letter considers a subclass of t-symmetric error correcting/all unidirectional error detecting (t-SyEC/AUED) codes in which the information is represented in an m-out-of-k coded form, which thus can be regarded as virtually systematic for practical purposes. For t3, previous researchers proposed methods for constructing codes of this subclass which are either optimal or of asymptotically optimal order. This letter proposes a new method for constructing, for any values of t, m and k, codes that are either optimal or of asymptotically optimal order. The redundancy of the obtained code is of the order tlog2k bits when mt.