Abstract
In this paper, we design and develop a new class of linear algebraic codes defined as soft linear algebraic codes using soft sets. The advantage of using these codes is that they have the ability to transmit m-distinct messages to m-set of receivers simultaneously. The methods of generating and decoding these new classes of soft linear algebraic codes have been developed. The notion of soft canonical generator matrix, soft canonical parity check matrix, and soft syndrome are defined to aid in construction and decoding of these codes. Error detection and correction of these codes are developed and illustrated by an example.
Highlights
Shannon [1,2] published an historic paper that marked the beginning of both error correcting codes and information theory
Soft sets [14] have been developed to neutrosophic soft sets [15], soft neutrosophic groups [16], soft neutrosophic algebraic structures, and their generalization [17,18,19,20]
The generator matrix can be in any other form, and the parity check matrix can be found out by the usual methods given in Reference [11]
Summary
Shannon [1,2] published an historic paper that marked the beginning of both error correcting codes and information theory. Fuzzy codes and distance properties was developed by [10]. For literature used in this paper on coding theory, see Reference [11]. We define soft linear codes using soft sets. Soft sets [12] are generalization of fuzzy sets introduced in [13]. Relationship among soft sets and fuzzy sets was studied in Reference [20,21]. For the first time, soft set theory has been used in the construction of algebraic codes, which we choose to call as soft algebraic linear codes.
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