Information on Result #674296

Linear OA(358, 4782999, F3, 6) (dual of [4782999, 4782941, 7]-code), using construction X4 applied to Ce(6) ⊂ Ce(3) based on
  1. linear OA(357, 4782969, F3, 7) (dual of [4782969, 4782912, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [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(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
  4. linear OA(31, 30, F3, 1) (dual of [30, 29, 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(359, 4783000, F3, 6) (dual of [4783000, 4782941, 7]-code) [i]Code Embedding in Larger Space
2Linear OOA(358, 4782999, F3, 2, 6) (dual of [(4782999, 2), 9565940, 7]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(358, 4782999, F3, 3, 6) (dual of [(4782999, 3), 14348939, 7]-NRT-code) [i]
4Linear OOA(358, 4782999, F3, 4, 6) (dual of [(4782999, 4), 19131938, 7]-NRT-code) [i]
5Linear OOA(358, 4782999, F3, 5, 6) (dual of [(4782999, 5), 23914937, 7]-NRT-code) [i]
6Linear OOA(358, 1594333, F3, 3, 6) (dual of [(1594333, 3), 4782941, 7]-NRT-code) [i]OOA Folding
7Linear OOA(358, 1594333, F3, 4, 6) (dual of [(1594333, 4), 6377274, 7]-NRT-code) [i]OA Folding and Stacking
8Linear OOA(358, 1594333, F3, 5, 6) (dual of [(1594333, 5), 7971607, 7]-NRT-code) [i]