Information on Result #734429

Linear OA(3227, 2023, F32, 10) (dual of [2023, 1996, 11]-code), using (u, u+v)-construction based on
  1. linear OA(327, 993, F32, 5) (dual of [993, 986, 6]-code), using
  2. linear OA(3220, 1030, F32, 10) (dual of [1030, 1010, 11]-code), using
    • construction XX applied to C1 = C([1021,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([1021,7]) [i] based on
      1. linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      2. linear OA(3215, 1023, F32, 8) (dual of [1023, 1008, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,7}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      4. 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]
      5. linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
      6. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), 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 OOA(3227, 1011, F32, 2, 10) (dual of [(1011, 2), 1995, 11]-NRT-code) [i]OOA Folding