This paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. Then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. Finally an example is given to illustrate the performance of the methods.

this paper investigates existence and uniqueness results for the first order fuzzy integro-differential equations. then numerical results and error bound based on the left rectangular quadrature rule, trapezoidal rule and a hybrid of them are obtained. finally an example is given to illustrate the performance of the methods.

We assign binary and ternary error-correcting codes to the data of syntactic structures of world languages and we study the distribution of code points in the space of code parameters. We show that, while most codes populate the lower region approximating a superposition of Thomae functions, there is a substantial presence of codes above the Gilbert–Varshamov bound and even above the asymptotic...

We introduce and study a common generalization of 1-error binary perfect codes and perfect single error correcting codes in Lee metric, namely perfect codes on products of paths of length 2 and of infinite length. Both existence and nonexistence results are given.

MDS codes are codes meeting the Singleton bound. Both for theory and practice, these codes are very important and have been studied extensively. Codes near this bound, but not attaining it, have had far less attention. In this paper we study codes that almost reach the Singleton bound.

We prove the nonexistence of several four-dimensional codes over GF(8) that meet the Griesmer bound. The proofs use geometric methods based on the analysis of the weight structure of subcodes. The specific parameters of the codes ruled out are: [111, 4, 96], [110, 4, 95], [102, 4, 88], [101, 4, 87], [93, 4, 80], and the sequence [29 − j, 4, 24 − j], for j = 0, 1, 2.