Information on Result #702329

Linear OA(2147, 531, F2, 33) (dual of [531, 384, 34]-code), using construction XX applied to C1 = C([509,28]), C2 = C([0,30]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([509,30]) based on
  1. linear OA(2136, 511, F2, 31) (dual of [511, 375, 32]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  2. linear OA(2136, 511, F2, 31) (dual of [511, 375, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(2145, 511, F2, 33) (dual of [511, 366, 34]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,30}, and designed minimum distance d ≥ |I|+1 = 34 [i]
  4. linear OA(2127, 511, F2, 29) (dual of [511, 384, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
  5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-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 OA(2146, 530, F2, 32) (dual of [530, 384, 33]-code) [i]Truncation
2Linear OOA(2147, 265, F2, 2, 33) (dual of [(265, 2), 383, 34]-NRT-code) [i]OOA Folding
3Linear OOA(2147, 177, F2, 3, 33) (dual of [(177, 3), 384, 34]-NRT-code) [i]
4Linear OOA(2147, 132, F2, 4, 33) (dual of [(132, 4), 381, 34]-NRT-code) [i]
5Linear OOA(2147, 106, F2, 5, 33) (dual of [(106, 5), 383, 34]-NRT-code) [i]