Multiple-rate maximum rank distance codes

This paper proposes a coding scheme that derives a multiple-rate code from existing channel codes defined over the composite field and the ground field, where code length is fixed. Formally, from codes C
₁
(k, 1), C
₂
(k, 2),..., C
_k
(k, k) defined over GF(q) together with the code C(n,k) over GF(q
ⁿ
), the proposed scheme derives a multiple-rate code with fixed code length. The primary benefit of the proposed multiple-rate code is that it is equipped with a common encoding and decoding strategy. Identification of coded user messages of variable length are carried out through a simple procedure using orthogonal projectors.