Information on Result #686535

Linear OA(871, 262172, F8, 13) (dual of [262172, 262101, 14]-code), using construction X applied to Ce(12) ⊂ Ce(8) based on
  1. linear OA(867, 262144, F8, 13) (dual of [262144, 262077, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(843, 262144, F8, 9) (dual of [262144, 262101, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 262143 = 86−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(84, 28, F8, 3) (dual of [28, 24, 4]-code or 28-cap in PG(3,8)), 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(872, 262173, F8, 13) (dual of [262173, 262101, 14]-code) [i]Code Embedding in Larger Space
2Linear OOA(871, 262172, F8, 2, 13) (dual of [(262172, 2), 524273, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(871, 262172, F8, 3, 13) (dual of [(262172, 3), 786445, 14]-NRT-code) [i]
4Digital (58, 71, 262172)-net over F8 [i]
5Linear OA(872, 262174, F8, 13) (dual of [262174, 262102, 14]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OA(873, 262176, F8, 13) (dual of [262176, 262103, 14]-code) [i]
7Linear OOA(871, 131086, F8, 2, 13) (dual of [(131086, 2), 262101, 14]-NRT-code) [i]OOA Folding
8Linear OOA(871, 87390, F8, 3, 13) (dual of [(87390, 3), 262099, 14]-NRT-code) [i]
9Linear OOA(871, 43695, F8, 13, 13) (dual of [(43695, 13), 567964, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row