Information on Result #676045

Linear OA(398, 2214, F3, 20) (dual of [2214, 2116, 21]-code), using construction X applied to Ce(19) ⊂ Ce(15) based on
  1. linear OA(392, 2187, F3, 20) (dual of [2187, 2095, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
  2. linear OA(371, 2187, F3, 16) (dual of [2187, 2116, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
  3. linear OA(36, 27, F3, 3) (dual of [27, 21, 4]-code or 27-cap in PG(5,3)), 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(399, 2215, F3, 20) (dual of [2215, 2116, 21]-code) [i]Code Embedding in Larger Space
2Linear OOA(398, 1390, F3, 2, 20) (dual of [(1390, 2), 2682, 21]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
3Linear OOA(398, 1390, F3, 3, 20) (dual of [(1390, 3), 4072, 21]-NRT-code) [i]
4Linear OOA(398, 1390, F3, 4, 20) (dual of [(1390, 4), 5462, 21]-NRT-code) [i]
5Linear OOA(398, 1390, F3, 5, 20) (dual of [(1390, 5), 6852, 21]-NRT-code) [i]
6Digital (78, 98, 1390)-net over F3 [i]
7Linear OOA(398, 1107, F3, 2, 20) (dual of [(1107, 2), 2116, 21]-NRT-code) [i]OOA Folding
8Linear OOA(398, 738, F3, 3, 20) (dual of [(738, 3), 2116, 21]-NRT-code) [i]
9Linear OOA(398, 553, F3, 4, 20) (dual of [(553, 4), 2114, 21]-NRT-code) [i]
10Linear OOA(398, 442, F3, 5, 20) (dual of [(442, 5), 2112, 21]-NRT-code) [i]