Information on Result #682560

Linear OA(576, 78152, F5, 13) (dual of [78152, 78076, 14]-code), using construction XX applied to Ce(12) ⊂ Ce(8) ⊂ Ce(7) based on
  1. linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
  2. linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
  3. linear OA(543, 78125, F5, 8) (dual of [78125, 78082, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
  4. linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
  5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-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(576, 71551, F5, 2, 13) (dual of [(71551, 2), 143026, 14]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(576, 71551, F5, 3, 13) (dual of [(71551, 3), 214577, 14]-NRT-code) [i]
3Digital (63, 76, 71551)-net over F5 [i]
4Linear OOA(576, 39076, F5, 2, 13) (dual of [(39076, 2), 78076, 14]-NRT-code) [i]OOA Folding
5Linear OOA(576, 13025, F5, 13, 13) (dual of [(13025, 13), 169249, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row