Information on Result #682143

Linear OA(547, 1953136, F5, 7) (dual of [1953136, 1953089, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(5) based on
  1. linear OA(546, 1953125, F5, 7) (dual of [1953125, 1953079, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
  2. 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]
  3. linear OA(510, 11, F5, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,5)), using
  4. linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-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 OA(548, 1953137, F5, 7) (dual of [1953137, 1953089, 8]-code) [i]Code Embedding in Larger Space
2Linear OOA(547, 1755091, F5, 2, 7) (dual of [(1755091, 2), 3510135, 8]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(547, 1755091, F5, 3, 7) (dual of [(1755091, 3), 5265226, 8]-NRT-code) [i]
4Digital (40, 47, 1755091)-net over F5 [i]
5Linear OA(548, 1953138, F5, 7) (dual of [1953138, 1953090, 8]-code) [i]Construction X with VarÅ¡amov Bound
6Linear OOA(547, 976568, F5, 2, 7) (dual of [(976568, 2), 1953089, 8]-NRT-code) [i]OOA Folding
7Linear OOA(547, 651045, F5, 3, 7) (dual of [(651045, 3), 1953088, 8]-NRT-code) [i]
8Linear OOA(547, 651045, F5, 7, 7) (dual of [(651045, 7), 4557268, 8]-NRT-code) [i]OOA Folding and Stacking with Additional Row