Information on Result #708997

Linear OA(4198, 1070, F4, 50) (dual of [1070, 872, 51]-code), using construction XX applied to C1 = C([1018,40]), C2 = C([0,44]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1018,44]) based on
  1. linear OA(4171, 1023, F4, 46) (dual of [1023, 852, 47]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,40}, and designed minimum distance d ≥ |I|+1 = 47 [i]
  2. linear OA(4166, 1023, F4, 45) (dual of [1023, 857, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
  3. linear OA(4186, 1023, F4, 50) (dual of [1023, 837, 51]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,44}, and designed minimum distance d ≥ |I|+1 = 51 [i]
  4. linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
  5. linear OA(47, 27, F4, 4) (dual of [27, 20, 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(4199, 1071, F4, 50) (dual of [1071, 872, 51]-code) [i]Code Embedding in Larger Space
2Linear OOA(4198, 535, F4, 2, 50) (dual of [(535, 2), 872, 51]-NRT-code) [i]OOA Folding
3Linear OOA(4198, 356, F4, 3, 50) (dual of [(356, 3), 870, 51]-NRT-code) [i]