Method and apparatus for generating a set of generator polynomials for use as a tail biting convolutional code to operate on data transmitted over a channel comprises: (0) specifying a constraint and a low code rate for a tail biting convolutional code, where the low rate code is lower than 1/n (n being an integer greater than 4); (1) selecting valid combinations of generator polynomials to include in a pool of potential codes, each valid combination being a potential code of the low rate code; (2) determining first lines of a weight spectrum for each potential code in the pool and including potential codes of the pool having best first lines in a candidate set; (3) determining best codes of the candidate set based on the first L number of lines in the weight spectrum; (4) selecting an optimum code(s) from the best codes; and (5) configuring a circuit(s) of a data transceiver to implement the optimum code(s).