Information on Result #689060

Linear OA(989, 4783001, F9, 14) (dual of [4783001, 4782912, 15]-code), using construction X applied to Ce(13) ⊂ Ce(9) based on
  1. linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
  2. linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(990, 4783002, F9, 14) (dual of [4783002, 4782912, 15]-code) [i]Code Embedding in Larger Space
2Linear OA(991, 4783003, F9, 14) (dual of [4783003, 4782912, 15]-code) [i]
3Linear OOA(989, 4783001, F9, 2, 14) (dual of [(4783001, 2), 9565913, 15]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(989, 4783001, F9, 3, 14) (dual of [(4783001, 3), 14348914, 15]-NRT-code) [i]
5Digital (75, 89, 4783001)-net over F9 [i]
6Linear OA(990, 4783003, F9, 14) (dual of [4783003, 4782913, 15]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(991, 4783005, F9, 14) (dual of [4783005, 4782914, 15]-code) [i]
8Linear OOA(989, 2391500, F9, 2, 14) (dual of [(2391500, 2), 4782911, 15]-NRT-code) [i]OOA Folding
9Linear OOA(989, 1594333, F9, 3, 14) (dual of [(1594333, 3), 4782910, 15]-NRT-code) [i]
10Linear OOA(989, 683285, F9, 14, 14) (dual of [(683285, 14), 9565901, 15]-NRT-code) [i]OA Folding and Stacking