Information on Result #734452

Linear OA(3221, 2019, F32, 8) (dual of [2019, 1998, 9]-code), using (u, u+v)-construction based on
  1. linear OA(326, 992, F32, 4) (dual of [992, 986, 5]-code), using
  2. linear OA(3215, 1027, F32, 8) (dual of [1027, 1012, 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]) [i] based on
      1. linear OA(3213, 1023, F32, 7) (dual of [1023, 1010, 8]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
      2. linear OA(3213, 1023, F32, 7) (dual of [1023, 1010, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
      3. linear OA(3215, 1023, F32, 8) (dual of [1023, 1008, 9]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      4. linear OA(3211, 1023, F32, 6) (dual of [1023, 1012, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
      5. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
      6. linear OA(320, 2, F32, 0) (dual of [2, 2, 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(3221, 1009, F32, 2, 8) (dual of [(1009, 2), 1997, 9]-NRT-code) [i]OOA Folding