We describe a code lengthening technique that uses Unequal Error Protection codes as suux codes and combine it with iteration of the conventional Construction X. By applying this technique to BCH codes, we obtain 5 new binary codes, 13 new ternary codes and 13 new quaternary codes. An improvement of Construction XX yields 2 new ternary codes.

Ahstruct-It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial code in this class is shown to hav...

In this paper, we study a relative two-weight Z2Z4-additive codes. It is shown that the Gray image of a two-distance Z2Z4-additive code is a binary two-distance code and that the Gray image of a relative two-weight Z2Z4-additive code, with nontrivial binary part, is a linear binary relative two-weight code. The structure of relative two-weight Z2Z4-additive codes are described. Finally, we disc...

There is a classical lower bound on the dimension of a binary Goppa code. We survey results on some specific codes whose dimension exceeds this bound, and prove two conjectures on the true dimension of two classes of such codes.

We show that the binary Golay code is slightly more power efficient than the extended binary Golay code under maximum-likelihood (ML), hard-decision decoding. In fact, if a codeword from the extended code is transmitted, one cannot achieve a higher probability of correct decoding than by simply ignoring the 24th symbol and using an ML decoder for the non-extended code on the first 23 symbols. T...

Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57–72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that th...

A binary chain code for representing 3D curves is presented. 3D curves are digitalized and represented as 3D discrete curves. 3D discrete curves are composed of constant straight-line segments using only orthogonal directions. The proposed binary notation is based on the orthogonal direction change chain code. Thus, using the proposed binary chain code it is possible to represent any 3D curve b...