Weight Enumerator of the putative [70,35,14] Type I Code


It is easy to see that that the existence of a [72,36,16] Type II code is equivalent to the existence of a [70,35,14] Type I code whose shadow has minimum weight 15. It is also true that the only accepteable weight enumerator for a [70,35,14] Type I code has a shadow with minimum weight 15.



The weight enumerator of the [70,35,14] Type I code.



Number Weight
1 0
11730 14
150535 16
1345960 18
9393384 20
49991305 22
204312290 24
650311200 26
1627498400 28
3221810284 30
5066556495 32
6348487600 34
6348487600 36
5066556495 38
3221810284 40
1627498400 42
650311200 44
204312290 46
49991305 48
9393384 50
1345960 52
150535 54
11730 16
1 70




The weight enumerator of the shadow.




Number Weight
87584 15
7367360 19
208659360 23
2119532800 27
8314349120 31
13059745920 35
8314349120 39
2119532800 43
208659360 47
7367360 51
87584 55




This weight enumerator appeared incorrectly in [1].




[1] G. Kennedy and V.Pless, A Coding-Theoretic Approach to Extending Designs, Discrete Mathematics, 1995.






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