Finite Field and Linear Codes 1 Finite field
... Definition 3.1 (Linear code). A linear code C of length n over Zq is a subspace of Znq . Example 3.1. The following are linear codes: (i) The repetition code: C = {(λ, λ, ..., λ) : λ ∈ Zq , ∀ q}; (ii) C = {000, 001, 010, 011} over Z2 is a subspace of Z32 ; (iii) C = {0000, 1100, 2200, 0001, 0002, 11 ...
... Definition 3.1 (Linear code). A linear code C of length n over Zq is a subspace of Znq . Example 3.1. The following are linear codes: (i) The repetition code: C = {(λ, λ, ..., λ) : λ ∈ Zq , ∀ q}; (ii) C = {000, 001, 010, 011} over Z2 is a subspace of Z32 ; (iii) C = {0000, 1100, 2200, 0001, 0002, 11 ...
MATRIX TRANSFORMATIONS 1 Matrix Transformations
... Some of the most basic matrix operators on R3 are those that map each point into its symmetric image about a fixed plane. These are called reflection operators. The following diagrams show the standard matrices for the reflections about the coordinate planes in R3 . In each case the standard matrix ...
... Some of the most basic matrix operators on R3 are those that map each point into its symmetric image about a fixed plane. These are called reflection operators. The following diagrams show the standard matrices for the reflections about the coordinate planes in R3 . In each case the standard matrix ...
