Information on Result #707501

Linear OA(431, 1033, F4, 8) (dual of [1033, 1002, 9]-code), using construction XX applied to C1 = C([1022,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([1022,6]) based on
  1. linear OA(426, 1023, F4, 7) (dual of [1023, 997, 8]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. 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]
  3. linear OA(431, 1023, F4, 8) (dual of [1023, 992, 9]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
  4. linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
  5. linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
  6. linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code) (see above)

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(433, 1052, F4, 8) (dual of [1052, 1019, 9]-code) [i]VarÅ¡amov–Edel Lengthening
2Linear OA(434, 1100, F4, 8) (dual of [1100, 1066, 9]-code) [i]
3Linear OA(435, 1220, F4, 8) (dual of [1220, 1185, 9]-code) [i]
4Linear OOA(431, 516, F4, 2, 8) (dual of [(516, 2), 1001, 9]-NRT-code) [i]OOA Folding
5Linear OOA(431, 344, F4, 3, 8) (dual of [(344, 3), 1001, 9]-NRT-code) [i]