Information on Result #682414

Linear OA(589, 78152, F5, 15) (dual of [78152, 78063, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,5]) based on
  1. linear OA(585, 78126, F5, 15) (dual of [78126, 78041, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
  2. linear OA(557, 78126, F5, 11) (dual of [78126, 78069, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
  3. linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), 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(589, 76346, F5, 2, 15) (dual of [(76346, 2), 152603, 16]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(589, 76346, F5, 3, 15) (dual of [(76346, 3), 228949, 16]-NRT-code) [i]
3Digital (74, 89, 76346)-net over F5 [i]
4Linear OOA(589, 39076, F5, 2, 15) (dual of [(39076, 2), 78063, 16]-NRT-code) [i]OOA Folding
5Linear OOA(589, 26050, F5, 3, 15) (dual of [(26050, 3), 78061, 16]-NRT-code) [i]