Simple rate-1/3 convolutional and tail-biting quantum error-correcting codes

Simple rate-1/3 single-error-correcting unrestricted and CSS-type quantum convolutional codes are constructed from classical self-orthogonal F₄-linear and F₂-linear convolutional codes, respectively. These quantum convolutional codes have higher rate than comparable quantum block codes or previous quantum convolutional codes, and are simple to decode. A block single-error-correcting [9,3,3] tail-biting code is derived from the unrestricted convolutional code, and similarly a [15,5,3] CSS-type block code from the CSS-type convolutional code