Information on Result #729303

Linear OA(32105, 1036, F32, 53) (dual of [1036, 931, 54]-code), using construction XX applied to C1 = C([1019,47]), C2 = C([0,48]), C3 = C1 + C2 = C([0,47]), and C∩ = C1 ∩ C2 = C([1019,48]) based on
  1. linear OA(32100, 1023, F32, 52) (dual of [1023, 923, 53]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−4,−3,…,47}, and designed minimum distance d ≥ |I|+1 = 53 [i]
  2. linear OA(3294, 1023, F32, 49) (dual of [1023, 929, 50]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,48], and designed minimum distance d ≥ |I|+1 = 50 [i]
  3. linear OA(32102, 1023, F32, 53) (dual of [1023, 921, 54]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−4,−3,…,48}, and designed minimum distance d ≥ |I|+1 = 54 [i]
  4. linear OA(3292, 1023, F32, 48) (dual of [1023, 931, 49]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,47], and designed minimum distance d ≥ |I|+1 = 49 [i]
  5. linear OA(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), 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(32105, 518, F32, 2, 53) (dual of [(518, 2), 931, 54]-NRT-code) [i]OOA Folding