Title: Weight Spectrum of Quasi-Perfect Binary Codes with Distance 4,
Abstract: We consider the weight spectrum of a class of quasi-perfect binary linear
codes with code distance 4. For example, extended Hamming code and Panchenko
code are the known members of this class. Also, it is known that in many cases
Panchenko code has the minimal number of weight 4 codewords. We give exact
recursive formulas for the weight spectrum of quasi-perfect codes and their
dual codes. As an example of application of the weight spectrum we derive a
lower estimate for the conditional probability of correction of erasure
patterns of high weights (equal to or greater than code distance).