On new completely regular q-ary codes

In this paper from q-ary perfect codes new completely regular q-ary codes are constructed. In particular, two new ternary completely regular codes are obtained from ternary Golay [11, 6, 5] code. The first [11, 5, 6] code with covering radius ρ = 4 coincides with the dual Golay code and its intersection array is (22, 20, 18, 2, 1; 1, 2, 9, 20, 22) . The second [10, 5, 5] code, with covering radius ρ = 4, coincides with the dual code of the punctured dual Golay code and has the intersection array given by (20, 18, 4, 1; 1, 2, 18, 20). New q-ary completely regular codes are obtained from q-ary perfect codes with d = 3. It is shown that under certain conditions a q-ary perfect (n,N, 3) code gives a new q-ary completely regular code with d = 4, covering radius ρ = 3 and intersection array (n(q − 1), (n− 1)(q − 1), 1; 1, (n− 1), n(q − 1)). For the case q = 2, (m ≥ 2) this gives, in particular, an infinite family of new q-ary completely regular [q + 1, q − 2, 4] codes with covering radius ρ = 3 and with intersection array (q − 1, q(q − 1), 1; 1, q, q − 1). Any q-ary perfect (n,N, 3) code gives a new completely regular (n−1, N/q, 3) code with covering radius ρ = 2 and intersection array ((n − 1)(q − 1), (q − 1); 1, (n − 1(q − 1)).