ABSTRACT
Since most ECCs are matrix codes, we present their common features about encoding and decoding and discuss certain special codes, which will be useful later in defining other important codes.
9.1 Matrix Group Codes
We use modulo 2 arithmetic. Let Fn 2 denote the binary n-tuples of the form
a = (a1, a2, . . . , an) : ai = 0 or 1 for i = 1, . . . , n. Then the properties of matrix codes are:
1. An (m,n) code K is a one-to-one function K : X ⊂ Fm 2 7→ Fn
2 , n ≥ m.
