On New Completely Regular $q$-ary Codes

In this paper, new completely regular $q$-ary codes are constructed from $q$-ary perfect codes. In particular, several new ternary completely regular codes are obtained from the ternary $[11,6,5]$ Golay code. One of these codes with parameters $[11,5,6]$ has covering radius $\rho=5$ and intersection array $(22,20,18,2,1;1,2,9,20,22)$. This code is dual to the ternary perfect $[11,6,5]$ Golay code. Another $[10,5,5]$ code has covering radius $\rho=4$ and intersection array $(20,18,4,1;1,2,18,20)$. This code is obtained by deleting one position of the former code. All together, the ternary Golay code results in eight completely regular codes, only four of which were previously known. Also, new infinite families of completely regular codes are constructed from $q$-ary Hamming codes.