Information on Result #699768

Linear OA(12825, 2097167, F128, 8) (dual of [2097167, 2097142, 9]-code), using construction X applied to Ce(7) ⊂ Ce(3) based on
  1. linear OA(12822, 2097152, F128, 8) (dual of [2097152, 2097130, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), 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 OOA(12825, 2097167, F128, 2, 8) (dual of [(2097167, 2), 4194309, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(12825, 2097167, F128, 3, 8) (dual of [(2097167, 3), 6291476, 9]-NRT-code) [i]
3Linear OOA(12825, 2097167, F128, 4, 8) (dual of [(2097167, 4), 8388643, 9]-NRT-code) [i]
4Digital (17, 25, 2097167)-net over F128 [i]
5Linear OOA(12825, 1048583, F128, 2, 8) (dual of [(1048583, 2), 2097141, 9]-NRT-code) [i]OOA Folding
6Linear OOA(12825, 699055, F128, 3, 8) (dual of [(699055, 3), 2097140, 9]-NRT-code) [i]
7Linear OOA(12825, 524291, F128, 4, 8) (dual of [(524291, 4), 2097139, 9]-NRT-code) [i]
8Linear OOA(12825, 524291, F128, 8, 8) (dual of [(524291, 8), 4194303, 9]-NRT-code) [i]OA Folding and Stacking