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We obtain a characterization on self-orthogonality for a given binary linear code in terms of the number of column vectors in its generator matrix, which extends the result of Bouyukliev et al. (2006). As an application, we give an algorithmic method to embed a given binary k-dimensional linear code C (k = 3,4) into a self-orthogonal code of the shortest length which has the same dimension k and minimum distance d' ≥ d(C). For k > 4, we suggest a recursive method to embed a k -dimensional linear code to a self-orthogonal code. We also give new explicit formulas for the minimum distances of optimal self-orthogonal codes for any length n with dimension 4 and any length n ≢ 6, 13,14,21,22,28,29 (mod 31) with dimension 5. [ABSTRACT FROM AUTHOR]

We present new constructions of codes for asymmetric channels for both binary and nonbinary alphabets, based on methods of generalized code concatenation. For the binary asymmetric channel, our methods construct nonlinear single-error-correcting codes from ternary outer codes. We show that some of the Varshamov–Tenengol’ts–Constantin–Rao codes, a class of binary nonlinear codes for this channel, have a nice structure when viewed as ternary codes. In many cases, our ternary construction yields even better codes. For the nonbinary asymmetric channel, our methods construct linear codes for many lengths and distances which are superior to the linear codes of the same length capable of correcting the same number of symmetric errors. [ABSTRACT FROM AUTHOR]