Information on Result #737021

Linear OA(3177, 6617, F3, 31) (dual of [6617, 6440, 32]-code), using construction X applied to Ce(30) ⊂ Ce(22) based on
  1. linear OA(3161, 6561, F3, 31) (dual of [6561, 6400, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(3121, 6561, F3, 23) (dual of [6561, 6440, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 6560 = 38−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(316, 56, F3, 7) (dual of [56, 40, 8]-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(3179, 6619, F3, 31) (dual of [6619, 6440, 32]-code) [i]Code Embedding in Larger Space
2Linear OA(3176, 6616, F3, 30) (dual of [6616, 6440, 31]-code) [i]Truncation
3Linear OOA(3177, 4562, F3, 2, 31) (dual of [(4562, 2), 8947, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
4Linear OOA(3177, 4562, F3, 3, 31) (dual of [(4562, 3), 13509, 32]-NRT-code) [i]
5Linear OOA(3177, 4562, F3, 4, 31) (dual of [(4562, 4), 18071, 32]-NRT-code) [i]
6Linear OOA(3177, 4562, F3, 5, 31) (dual of [(4562, 5), 22633, 32]-NRT-code) [i]
7Digital (146, 177, 4562)-net over F3 [i]
8Linear OOA(3177, 3308, F3, 2, 31) (dual of [(3308, 2), 6439, 32]-NRT-code) [i]OOA Folding
9Linear OOA(3177, 2205, F3, 3, 31) (dual of [(2205, 3), 6438, 32]-NRT-code) [i]
10Linear OOA(3177, 1654, F3, 4, 31) (dual of [(1654, 4), 6439, 32]-NRT-code) [i]
11Linear OOA(3177, 1323, F3, 5, 31) (dual of [(1323, 5), 6438, 32]-NRT-code) [i]