Information on Result #708589

Linear OA(4163, 1066, F4, 41) (dual of [1066, 903, 42]-code), using construction XX applied to C1 = C([1019,32]), C2 = C([1,36]), C3 = C1 + C2 = C([1,32]), and C∩ = C1 ∩ C2 = C([1019,36]) based on
  1. linear OA(4136, 1023, F4, 37) (dual of [1023, 887, 38]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,32}, and designed minimum distance d ≥ |I|+1 = 38 [i]
  2. linear OA(4135, 1023, F4, 36) (dual of [1023, 888, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
  3. linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,36}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(4120, 1023, F4, 32) (dual of [1023, 903, 33]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
  5. linear OA(47, 23, F4, 4) (dual of [23, 16, 5]-code), using
  6. linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), 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(4164, 1067, F4, 41) (dual of [1067, 903, 42]-code) [i]Code Embedding in Larger Space
2Linear OA(4165, 1068, F4, 41) (dual of [1068, 903, 42]-code) [i]
3Linear OOA(4163, 533, F4, 2, 41) (dual of [(533, 2), 903, 42]-NRT-code) [i]OOA Folding
4Linear OOA(4163, 355, F4, 3, 41) (dual of [(355, 3), 902, 42]-NRT-code) [i]