Even before the search for the weight 12 codeword was finished, we were looking for a way to solve the whole problem. One possibility is to determine and then the weight enumerator. Unless the weight enumerator provides a contradiction, we still have to perform another search. Hall in [14] proved that if , then there exist primitive weight 20 codewords, which intersect the lines of the plane in at most four points. We might be able to skip the step of finding if we could go directly to weight 20. Unfortunately, we obtained an estimate of at least weight 20 starting configurations. Even though, as Hall remarked, it required only a few minutes of computer time to try each starting configuration, a few minutes times equaled years --- clearly beyond our capability. There was no short cut which could avoid computing the weight enumerator.
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