Justesen first constructed asymptotically good concatenated codes such that the outer code is Reed-Solomon (RS) code and the inner code is Wozencraft's ensemble of randomly shifted codes. Kolev gave the weight distributions of Justesen codes in some cases. In this paper, we give the weight distributions of Justesen codes obtained by using some other RS codes as the outer code.

Recently, Vatan, Roychowdhury and Anantram have presented two types of revised versions of the Calderbank-Shor-Steane code construction, and have also provided an exhaustive procedure for determining bases of quantum error-correcting codes. In this paper, we investigate the revised versions given by Vatan et al., and point out that there is no essential difference between them. In addition, we propose an efficient algorithm for searching for bases of quantum error-correcting codes. The proposed algorithm is based on some fundamental properties of classical linear codes, and has much lower complexity than Vatan et al.'s procedure.

Coding scheme is discussed for M-Choose-T communication in which at most T active users out of M potential users simultaneously transmit their messages over a common channel. The multiple-access channel considered in this paper is assumed to be a time-discrete noiseless adder channel without feedback with T binary inputs and one real-valued output, and is used on the assumption of perfect block and bit synchronization among users. In this paper a new class of uniquely decodable codes is proposed in order to realize error-free M-Choose-T communication over the adder channel described above. These codes are uniquely decodable in the sense that not only the set of active users can be specified but also their transmitted messages can be recovered uniquely as long as T or fewer users are active simultaneously. It is shown that these codes have a simple decoding algorithm and can achieve a very high sum rate arbitrarily close to unity if exactly T users are active.