ABSTRACT
We will assume that the reader is familiar with the definition and properties of a vector (linear) space and finite field Fq, which is simply a subspace of the vector space Fn
q . Linear codes C are vector spaces and their algebraic
structures follow the rules of a linear space. Some examples of vector spaces over Fq are:
(i) For any q, C1 = F n
q , and C2 = {0} = the zero vector (0, 0, . . . , 0) ∈ F
q ;
(ii) For any q, C3 = {(λ, . . . , λ) : λ ∈ F n
q };
(iii) For q = 2, C4 = {(0, 0, 0, 0, ), (1, 0, 1, 0), (0, 1, 0, 1), (1, 1, 1, 1)};
(iv) For q = 3, C5 = {(0, 0, 0), (0, 1, 2), (0, 2, 1)}.
