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MDS code is a linear code that achieves equality in the Singleton bound, and projective MDS (PG-MDS) is MDS code with independents property of any two columns of its generator matrix. In this paper, elementary methods for modifying a PG-MDS code of dimensions 2, 3, as extending and lengthening, in order to find new incomplete PG-MDS codes have been used over . Also, two complete PG-MDS codes over of length and 28 have been found.

The local resolving neighborhood of a pair of vertices for and is if there is a vertex in a connected graph where the distance from to is not equal to the distance from to , or defined by . A local resolving function of is a real valued function such that for and . The local fractional metric dimension of graph denoted by , defined by In this research, the author discusses about the local fractional metric dimension of comb product are two graphs, namely graph and graph , where graph is a connected graphs and graph is a complate graph and denoted by We get

In this work, the notion of principally quasi- injective semimodule is introduced, discussing the conditions needed to get properties and characterizations similar or related to the case in modules. Let be an -semimodule with endomorphism semiring Ș. The semimodule is called principally quasi-injective, if every -homomorphism from any cyclic subsemimodule of to can be extended to an endomorphism of .