In this paper, we introduce the notion of complete joint Jacobi polynomial two linear codes length n over $${\mathbb {F}}_{q}$$ and {Z}}_{k}$$ . We give MacWilliams type identity for polynomials codes. also concepts average a representation in terms compositions its distribution Further present generalization $$(g+1)$$ -fold Finally, intersection number

For an odd prime p and each non-empty subset S ⊂ GF (p), consider the hyperelliptic curve XS defined by y = fS(x), where fS(x) = Q a∈S(x− a). Using a connection between binary quadratic residue codes and hyperelliptic curves over GF (p), this paper investigates how coding theory bounds give rise to bounds such as the following example: for all sufficiently large primes p there exists a subset S...

Propositional circumscription, asking for the minimal models of a Boolean formula, is an important problem in artificial intelligence, in data mining, in coding theory, and in the model checking based procedures in automated reasoning. We consider the counting problems of propositional circumscription for several subclasses with respect to the structure of the formula. We prove that the countin...

Concurrent checkers are commonly used in computer systems to detect computational errors on-line, which enhances reliability. Using the coding theory framework developed earlier by the authors, it is shown in the following that concurrent checkers, already available within the circuit, can be utilized very effectively during off-line testing. Specifically, test time as well as fault escape prob...