The original iterated codes proposed by P. Elias can be regarded as the codes constructed by iterating two dimensional product codes. While the modified product codes have been proposed and shown to be able to increase the rates without increasing the probability of decoding error. On the other hand, we have proposed new codes, called modified iterated codes A, and improved the performance for the original iterated codes by applying the coding and the decoding schemes of the modified product codes to these product codes. It has been proved that the rates of codes A were always much higher than those of the original iterated codes for cross-over probability p0.1617. In this paper, by additionally combining the coding and the decoding schemes of the superimposed codes constructed on the basis of the modified product codes, which are able to increase the rates with the same minimum distance, the performance for codes A can be further improved. We call codes thus constructed modified iterated codes B. It is shown that the rates of codes B are partially higher than those of codes A for p0.0959.

Concatenated codes have many remarkable properties from both the theoretical and practical viewpoints. The minimum distance of a concatenated code is at least the product of the minimum distances of an outer code and an inner code. In this paper, we shall study on a condition that the minimum distance of concatenated codes is beyond the lower bound.

Concatenated codes have many remarkable properties from both the theoretical and practical viewpoints. The minimum distance of a concatenated code is at least the product of the minimum distances of an outer code and an inner code. In this paper, we shall examine some cases that the minimum distance of concatenated codes is beyond the lower bound and get the tighter bound or the true minimum distance of concatenated codes by using the complete weight enumerator of the outer code and the Hamming weight enumerator of the inner code. Furthermore we propose a new decoding method based on Reddy-Robinson algorithm by using the decoding method beyond the BCH bound.

In this paper, the existential lower bounds on asymptotic distance ratios of error-correcting codes with J(J2) levels of unequal error protection given by encoding and decoding methods based on the concept of the generalized concatenated codes are obtained. The constructive concatenated codes with unequal error protection are proposed for high and low code rates. The formaer is constructed by the generalized version of Justesen codes. The latter is constructed by the secondorder concatenation with the generalized concatenated codes. Comparing the existential lower bounds on asymptotic distance ratios with those of the constructive concatenated codes, the lower bounds of the constructive codes are lower than the existential lower bounds.