Information on Result #674545

Linear OA(338, 531455, F3, 5) (dual of [531455, 531417, 6]-code), using construction X4 applied to Ce(4) ⊂ Ce(3) based on
  1. linear OA(337, 531441, F3, 5) (dual of [531441, 531404, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  2. linear OA(325, 531441, F3, 4) (dual of [531441, 531416, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(313, 14, F3, 13) (dual of [14, 1, 14]-code or 14-arc in PG(12,3)), using
  4. linear OA(31, 14, F3, 1) (dual of [14, 13, 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 OOA(338, 531455, F3, 2, 5) (dual of [(531455, 2), 1062872, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(338, 531455, F3, 3, 5) (dual of [(531455, 3), 1594327, 6]-NRT-code) [i]
3Linear OOA(338, 531455, F3, 4, 5) (dual of [(531455, 4), 2125782, 6]-NRT-code) [i]
4Linear OOA(338, 265727, F3, 2, 5) (dual of [(265727, 2), 531416, 6]-NRT-code) [i]OOA Folding
5Linear OOA(338, 265727, F3, 3, 5) (dual of [(265727, 3), 797143, 6]-NRT-code) [i]OOA Folding and Stacking with Additional Row
6Linear OOA(338, 265727, F3, 4, 5) (dual of [(265727, 4), 1062870, 6]-NRT-code) [i]
7Linear OOA(338, 265727, F3, 5, 5) (dual of [(265727, 5), 1328597, 6]-NRT-code) [i]