A study on some punctured codes of simplex codes

Abstract

Algebraic Coding Theory over finite fields and rings plays a prominent and pivotal newlinerole in the Information Theory. It has broad applications, including secret sharing newlineschemes, strongly regular graphs, authentication, and communication codes. In this newlinethesis, we have focused mainly on several research topics related to Algebraic Coding newlineTheory and its applications, particularly on constructing codes. We have constructed newlinesome new codes from puncturing the Zq-Simplex code called unit Zq-Simplex code, unit newlineZq-MacDonald code, unit Zq-Simplex code of type and#945; and zero divisor Zq-Simplex code. newlineUsing the conventional combinatorics approach, we have established their parameters newlineand weight distributions under the Hamming metric. Also, we have constructed classes newlineof few weight linear codes over Zpm for m = 2 and 3 under the Homogeneous weight newlinemetric. The Gray images of some class of these codes over Zpm are p-ary nonlinear codes, newlinewhich have the same weight distributions as those of the two-weight p-ary linear codes newlineof type SU1 in the sense of Calderbank and Kantor[The geometry of two-weight codes, newlineBull. London Math. Soc. 18(2) (1986) 97 122]. The Gray images of a specific class newlineof linear codes over Zp2 are found to be optimal projective linear codes over F2, which newlinesatisfies the Griesmer bound. Moreover, we have examined certain optimal projective newlinelinear codes over Zp3 concerning Plotkin-Type Bound when p = 2. Further, we have newlineexplored the applications in strongly regular graphs and secret sharing schemes. newline newline