Information on Result #707541

Linear OA(443, 1040, F4, 11) (dual of [1040, 997, 12]-code), using construction XX applied to C1 = C([1021,6]), C2 = C([0,8]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([1021,8]) based on
  1. linear OA(436, 1023, F4, 9) (dual of [1023, 987, 10]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
  2. linear OA(431, 1023, F4, 9) (dual of [1023, 992, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
  3. linear OA(441, 1023, F4, 11) (dual of [1023, 982, 12]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
  4. linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(443, 885, F4, 2, 11) (dual of [(885, 2), 1727, 12]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(443, 885, F4, 3, 11) (dual of [(885, 3), 2612, 12]-NRT-code) [i]
3Digital (32, 43, 885)-net over F4 [i]
4Linear OA(444, 1042, F4, 11) (dual of [1042, 998, 12]-code) [i]Construction X with VarÅ¡amov Bound
5Linear OOA(443, 520, F4, 2, 11) (dual of [(520, 2), 997, 12]-NRT-code) [i]OOA Folding
6Linear OOA(443, 346, F4, 3, 11) (dual of [(346, 3), 995, 12]-NRT-code) [i]