Optimum codes of dimension 3 and 4 over GF(4)

On the covering radius of Simplex codes

“…If G k (q) is a generator matrix for S k (q) , then a generator matrix for S k+1 (q) is given by (2). Thus if x ∈ F n q with d(x, S k (q)) = R(S k (q)) , then the distance of the word y = (x, 1, x, .…”

“…We prove it by induction on k . If G k (q) is a generator matrix for S k (q) , then a generator matrix G k+1 (q) for S k+1 (q) is given by (2). S k+1 (q) is equivalent to the code generated by the matrix…”

New bounds for n4(k,d) and classification of some optimal codes over GF(4)

“…Landjev solved the last unknown cases for q = 3 and k = 5 [24]. The quaternary case was considered, e.g., in [2,9,14,15,17,21,23,25,26]. Recent results on n 4 (5; d) can be found in [25,28].…”