Information on Result #682169

Linear OA(540, 1953146, F5, 6) (dual of [1953146, 1953106, 7]-code), using construction X applied to Ce(5) ⊂ Ce(2) based on
  1. linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
  2. linear OA(519, 1953125, F5, 3) (dual of [1953125, 1953106, 4]-code or 1953125-cap in PG(18,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
  3. linear OA(53, 21, F5, 2) (dual of [21, 18, 3]-code), 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(540, 1953146, F5, 2, 6) (dual of [(1953146, 2), 3906252, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(540, 1953146, F5, 3, 6) (dual of [(1953146, 3), 5859398, 7]-NRT-code) [i]
3Digital (34, 40, 1953146)-net over F5 [i]
4Linear OOA(540, 976573, F5, 2, 6) (dual of [(976573, 2), 1953106, 7]-NRT-code) [i]OOA Folding
5Linear OOA(540, 651048, F5, 3, 6) (dual of [(651048, 3), 1953104, 7]-NRT-code) [i]
6Linear OOA(540, 651048, F5, 6, 6) (dual of [(651048, 6), 3906248, 7]-NRT-code) [i]OA Folding and Stacking