Convolutional encoding of 60, 64, 68, 72-bit self-dual codes

In this paper we obtain [60,30,12], [64,32,12], [68,34,12], [72,36,12] doubly even self-dual codes as tailbitting convolutional codes with the smallest constraint length K=9. In this construction one information bit is modulo two add to the one of the encoder outputs and this row will replace the first row in the double circulant matrix. The pure double circulant construction with K=10 is also available for [68,34,12] and [72,36,12] codes. Keywords—convolutional encoding; double circulant; weight enumerator; tailbitting