On the minimum distance of some quadratic residue codes (Corresp.)

We find the minimum distances of the binary
(113, 57)
, and ternary
(37, 19), (61, 31), (71, 36)
, and
(73, 37)
quadratic residue codes and the corresponding extended codes. These distances are
15, 10, 11, 17
, and
17
, respectively, for the nonextended codes and are increased by one for the respective extended codes. We also characterize the minimum weight codewords for the
(113, 57)
binary code and its extended counterpart.