Information on Result #731849

Linear OA(430, 1050, F4, 7) (dual of [1050, 1020, 8]-code), using (u, u+v)-construction based on
  1. linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
  2. linear OA(426, 1033, F4, 7) (dual of [1033, 1007, 8]-code), using
    • construction XX applied to C1 = C([1022,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([1022,5]) [i] based on
      1. linear OA(421, 1023, F4, 6) (dual of [1023, 1002, 7]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
      2. 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]
      3. 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]
      4. linear OA(416, 1023, F4, 5) (dual of [1023, 1007, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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 OOA(430, 525, F4, 2, 7) (dual of [(525, 2), 1020, 8]-NRT-code) [i]OOA Folding