A linear code of block length n possessing minimum weight d has one code word of weight zero, and no other code words of weight less thand. The weight distribution of the code is given by the set of allW(j), d \leq j \leq n, describing the number of code words having a weight of exactlyj. Exact weight distributions are known for only a handful of linear codes. This paper presents an explicit upper bound uponW(j)as a function ofn, d, andj. The bound has general applicability to all linear codes.

The sensitivity of a binary block code to loss of synchronism (misplacement of the "commas" separating codewords) can be characterized by a pair of numbers[s, \delta]such that any synchronization slip of s bits or less produces an overlap sequence differing from a legitimate codeword in at least\deltaplaces. This definition is broader than that of comma freedom of index\delta, which is included as the special case of s equal to the integer part of half the code block length. For codes having the slip-detecting characteristic[s, \delta]there exists the possibility of implementation to restore synchronism during an interval relatively free from bit errors. It is shown that certain error-correcting binary cyclic block codes can be altered to obtain the characteristic[s, \delta]by the addition of a fixed binary vector to each codeword prior to transmission. These altered cyclic codes retain the full error-correcting power of the original cyclic codes. An error-detecting/correcting data format providing protection against the acceptance of misframed data is thus obtained without the insertion of special synchronizing sequences into the bit stream.