...ractable case of a binary symmetric channel. In Section 2, we review some of the main properties of the problem. (For an account of the history of contributions to the problem, we refer the reader to =-=[3]-=- and the references contained therein.) In Section 3, we present new demonstrations of results for general classes of codes. We construct an infinite class of codes that have non-systematic optimal ge...

...e rule for determining which codeword (which in turn determines which set of k information bits) will be chosen by the decoder given a particular received word. Consider for illustrative purposes the =-=[5; 3;2]-=- code with generator matrix G = 0 @ 1 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 A : The standard array is 00000 10011 01010 00101 11001 10110 01111 11100 00001 10010 01011 00100 11000 10111 01110 11101 00010 1000...

...t be wide-sense systematic. 3.2 The noisy region We present a simplified demonstration of the following results, which were first found in a more general form by Kiely, Coffey, and Bell [3]. Delsarte =-=[1]-=- had previously noted, via direct computation of half-coset weight enumerators, that the `ignore parity checks' decoding rule is optimum for many codes for sufficiently high p when the generator matri...