Neutrosophic Quadruple Algebraic Codes over Z2 and their Properties

Abstract

In this paper we for the first time develop, define and describe a new class of algebraic codes using Neutrosophic Quadruples which uses the notion of known value, and three unknown triplets (T, I, F) where T is the truth value, I is the indeterminate and F is the false value. Using this Neutrosophic Quadruples several researchers have built groups, NQ-semigroups, NQ-vector spaces and NQ-linear algebras. However, so far NQ algebraic codes have not been developed or defined. These NQ-codes have some peculiar properties like the number of message symbols are always fixed as 4-tuples, that is why we call them as Neutrosophic Quadruple codes. Here only the check symbols can vary according to the wishes of the researchers. Further we find conditions for two NQ-Algebraic codewords to be orthogonal. In this paper we study these NQ codes only over the field Z2. However, it can be carried out as a matter of routine in case of any field Zp of characteristics p.

Keywords

• neutrosophic quadruples; nq-vector spaces; nq-groups; neutrosophic quadruple algebraic codes (nq-algebraic codes); dual nq-algebraic codes; orthogonal nq- algebraic codes; nq generator matrix; parity check matrix; self dual nq algebraic codes