Information on Result #676019

Linear OA(3176, 2214, F3, 37) (dual of [2214, 2038, 38]-code), using construction X applied to Ce(36) ⊂ Ce(31) based on
  1. linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(3148, 2187, F3, 32) (dual of [2187, 2039, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
    • an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [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 OOA(3176, 1658, F3, 2, 37) (dual of [(1658, 2), 3140, 38]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(3176, 1658, F3, 3, 37) (dual of [(1658, 3), 4798, 38]-NRT-code) [i]
3Linear OOA(3176, 1658, F3, 4, 37) (dual of [(1658, 4), 6456, 38]-NRT-code) [i]
4Linear OOA(3176, 1658, F3, 5, 37) (dual of [(1658, 5), 8114, 38]-NRT-code) [i]
5Digital (139, 176, 1658)-net over F3 [i]
6Linear OOA(3176, 1107, F3, 2, 37) (dual of [(1107, 2), 2038, 38]-NRT-code) [i]OOA Folding
7Linear OOA(3176, 738, F3, 3, 37) (dual of [(738, 3), 2038, 38]-NRT-code) [i]
8Linear OOA(3176, 553, F3, 4, 37) (dual of [(553, 4), 2036, 38]-NRT-code) [i]
9Linear OOA(3176, 442, F3, 5, 37) (dual of [(442, 5), 2034, 38]-NRT-code) [i]