Information on Result #734060

Linear OA(3266, 2054, F32, 23) (dual of [2054, 1988, 24]-code), using (u, u+v)-construction based on
  1. linear OA(3221, 1027, F32, 11) (dual of [1027, 1006, 12]-code), using
    • construction XX applied to C1 = C([1022,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1022,9]) [i] based on
      1. 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 = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
      3. linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
      4. linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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)
  2. linear OA(3245, 1027, F32, 23) (dual of [1027, 982, 24]-code), using
    • construction XX applied to C1 = C([1022,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1022,21]) [i] based on
      1. linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
      2. linear OA(3243, 1023, F32, 22) (dual of [1023, 980, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
      3. linear OA(3245, 1023, F32, 23) (dual of [1023, 978, 24]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
      4. linear OA(3241, 1023, F32, 21) (dual of [1023, 982, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
      5. linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code) (see above)
      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(3266, 1027, F32, 2, 23) (dual of [(1027, 2), 1988, 24]-NRT-code) [i]OOA Folding