Information on Result #708289

Linear OA(4118, 1040, F4, 31) (dual of [1040, 922, 32]-code), using construction XX applied to C1 = C([1021,26]), C2 = C([0,28]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([1021,28]) based on
  1. linear OA(4111, 1023, F4, 29) (dual of [1023, 912, 30]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,26}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(4106, 1023, F4, 29) (dual of [1023, 917, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
  3. linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  4. linear OA(4101, 1023, F4, 27) (dual of [1023, 922, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  5. linear OA(41, 11, F4, 1) (dual of [11, 10, 2]-code), using
  6. linear OA(41, 6, F4, 1) (dual of [6, 5, 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 OOA(4118, 1023, F4, 2, 31) (dual of [(1023, 2), 1928, 32]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(4118, 1023, F4, 3, 31) (dual of [(1023, 3), 2951, 32]-NRT-code) [i]
3Digital (87, 118, 1023)-net over F4 [i]
4Linear OA(4119, 1042, F4, 31) (dual of [1042, 923, 32]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(4118, 520, F4, 2, 31) (dual of [(520, 2), 922, 32]-NRT-code) [i]OOA Folding
6Linear OOA(4118, 346, F4, 3, 31) (dual of [(346, 3), 920, 32]-NRT-code) [i]