Information on Result #674741

Linear OA(3207, 177188, F3, 28) (dual of [177188, 176981, 29]-code), using construction X applied to Ce(27) ⊂ Ce(22) based on
  1. linear OA(3199, 177147, F3, 28) (dual of [177147, 176948, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(3166, 177147, F3, 23) (dual of [177147, 176981, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 177146 = 311−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
  3. linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
    • the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]

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(3207, 177188, F3, 27) (dual of [177188, 176981, 28]-code) [i]Strength Reduction
2Linear OA(3208, 177189, F3, 28) (dual of [177189, 176981, 29]-code) [i]Code Embedding in Larger Space
3Linear OA(3209, 177190, F3, 28) (dual of [177190, 176981, 29]-code) [i]
4Linear OA(3206, 177187, F3, 27) (dual of [177187, 176981, 28]-code) [i]Truncation
5Linear OOA(3207, 88594, F3, 2, 28) (dual of [(88594, 2), 176981, 29]-NRT-code) [i]OOA Folding
6Linear OOA(3207, 59062, F3, 3, 28) (dual of [(59062, 3), 176979, 29]-NRT-code) [i]
7Linear OOA(3207, 44297, F3, 4, 28) (dual of [(44297, 4), 176981, 29]-NRT-code) [i]
8Linear OOA(3207, 35437, F3, 5, 28) (dual of [(35437, 5), 176978, 29]-NRT-code) [i]
9Linear OOA(3207, 12656, F3, 28, 28) (dual of [(12656, 28), 354161, 29]-NRT-code) [i]OA Folding and Stacking