Information on Result #702228

Linear OA(284, 531, F2, 19) (dual of [531, 447, 20]-code), using construction XX applied to C1 = C([509,14]), C2 = C([0,16]), C3 = C1 + C2 = C([0,14]), and C∩ = C1 ∩ C2 = C([509,16]) based on
  1. linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
  2. linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
  4. linear OA(264, 511, F2, 15) (dual of [511, 447, 16]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [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(283, 530, F2, 18) (dual of [530, 447, 19]-code) [i]Truncation
2Linear OOA(284, 265, F2, 2, 19) (dual of [(265, 2), 446, 20]-NRT-code) [i]OOA Folding
3Linear OOA(284, 177, F2, 3, 19) (dual of [(177, 3), 447, 20]-NRT-code) [i]
4Linear OOA(284, 132, F2, 4, 19) (dual of [(132, 4), 444, 20]-NRT-code) [i]
5Linear OOA(284, 106, F2, 5, 19) (dual of [(106, 5), 446, 20]-NRT-code) [i]
6Linear OOA(284, 88, F2, 6, 19) (dual of [(88, 6), 444, 20]-NRT-code) [i]
7Linear OOA(284, 75, F2, 7, 19) (dual of [(75, 7), 441, 20]-NRT-code) [i]