Information on Result #674275

Linear OA(344, 4782985, F3, 5) (dual of [4782985, 4782941, 6]-code), using construction X4 applied to Ce(4) ⊂ Ce(3) based on
  1. linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
  2. linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
  3. linear OA(315, 16, F3, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,3)), using
  4. linear OA(31, 16, F3, 1) (dual of [16, 15, 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(344, 4782985, F3, 2, 5) (dual of [(4782985, 2), 9565926, 6]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(344, 4782985, F3, 3, 5) (dual of [(4782985, 3), 14348911, 6]-NRT-code) [i]
3Linear OOA(344, 4782985, F3, 4, 5) (dual of [(4782985, 4), 19131896, 6]-NRT-code) [i]
4Linear OOA(344, 2391492, F3, 2, 5) (dual of [(2391492, 2), 4782940, 6]-NRT-code) [i]OOA Folding
5Linear OOA(344, 2391492, F3, 3, 5) (dual of [(2391492, 3), 7174432, 6]-NRT-code) [i]OOA Folding and Stacking with Additional Row
6Linear OOA(344, 2391492, F3, 4, 5) (dual of [(2391492, 4), 9565924, 6]-NRT-code) [i]
7Linear OOA(344, 2391492, F3, 5, 5) (dual of [(2391492, 5), 11957416, 6]-NRT-code) [i]