we present an approach to design of fault tolerant computing systems. in this paper, a technique is employed that enable the combination of several codes, in order to obtain flexibility in the design of error correcting codes. code combining techniques are very effective, which one of these codes are turbo codes. the algorithm-based fault tolerance techniques that to detect errors rely on the c...

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

The binary and ternary codes spanned by the rows of the point by block incidence matrices of some 2-designs and their complementary and orthogonal designs are studied. A new method is also introduced to study optimal codes.