Information on Result #734206

Linear OA(3252, 1124, F32, 19) (dual of [1124, 1072, 20]-code), using (u, u+v)-construction based on
  1. linear OA(3215, 97, F32, 9) (dual of [97, 82, 10]-code), using
    • construction XX applied to C1 = C([92,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([92,7]) [i] based on
      1. linear OA(3213, 93, F32, 8) (dual of [93, 80, 9]-code), using the BCH-code C(I) with length 93 | 322−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
      2. linear OA(3213, 93, F32, 8) (dual of [93, 80, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(3215, 93, F32, 9) (dual of [93, 78, 10]-code), using the BCH-code C(I) with length 93 | 322−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
      4. linear OA(3211, 93, F32, 7) (dual of [93, 82, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 93 | 322−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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(3237, 1027, F32, 19) (dual of [1027, 990, 20]-code), using
    • construction XX applied to C1 = C([1022,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([1022,17]) [i] based on
      1. linear OA(3235, 1023, F32, 18) (dual of [1023, 988, 19]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
      2. linear OA(3235, 1023, F32, 18) (dual of [1023, 988, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
      3. linear OA(3237, 1023, F32, 19) (dual of [1023, 986, 20]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
      4. linear OA(3233, 1023, F32, 17) (dual of [1023, 990, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(3252, 562, F32, 2, 19) (dual of [(562, 2), 1072, 20]-NRT-code) [i]OOA Folding