Information on Result #686422

Linear OA(8113, 262173, F8, 21) (dual of [262173, 262060, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
  1. linear OA(8109, 262145, F8, 21) (dual of [262145, 262036, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
  2. linear OA(885, 262145, F8, 17) (dual of [262145, 262060, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 812−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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(8114, 262174, F8, 21) (dual of [262174, 262060, 22]-code) [i]Code Embedding in Larger Space
2Linear OA(8115, 262175, F8, 21) (dual of [262175, 262060, 22]-code) [i]
3Linear OOA(8113, 238548, F8, 2, 21) (dual of [(238548, 2), 476983, 22]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(8113, 238548, F8, 3, 21) (dual of [(238548, 3), 715531, 22]-NRT-code) [i]
5Digital (92, 113, 238548)-net over F8 [i]
6Linear OA(8114, 262175, F8, 21) (dual of [262175, 262061, 22]-code) [i]Construction X with VarÅ¡amov Bound
7Linear OA(8115, 262177, F8, 21) (dual of [262177, 262062, 22]-code) [i]
8Linear OOA(8113, 131086, F8, 2, 21) (dual of [(131086, 2), 262059, 22]-NRT-code) [i]OOA Folding
9Linear OOA(8113, 87391, F8, 3, 21) (dual of [(87391, 3), 262060, 22]-NRT-code) [i]
10Linear OOA(8113, 26217, F8, 21, 21) (dual of [(26217, 21), 550444, 22]-NRT-code) [i]OOA Folding and Stacking with Additional Row