Information on Result #702816

Linear OA(2163, 1075, F2, 31) (dual of [1075, 912, 32]-code), using construction XX applied to C1 = C([1019,22]), C2 = C([0,26]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([1019,26]) based on
  1. linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  2. linear OA(2131, 1023, F2, 27) (dual of [1023, 892, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  3. linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  4. linear OA(2111, 1023, F2, 23) (dual of [1023, 912, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  5. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)), using
  6. linear OA(26, 26, F2, 3) (dual of [26, 20, 4]-code or 26-cap in PG(5,2)) (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(2162, 1074, F2, 30) (dual of [1074, 912, 31]-code) [i]Truncation
2Linear OOA(2163, 537, F2, 2, 31) (dual of [(537, 2), 911, 32]-NRT-code) [i]OOA Folding
3Linear OOA(2163, 358, F2, 3, 31) (dual of [(358, 3), 911, 32]-NRT-code) [i]
4Linear OOA(2163, 268, F2, 4, 31) (dual of [(268, 4), 909, 32]-NRT-code) [i]
5Linear OOA(2163, 215, F2, 5, 31) (dual of [(215, 5), 912, 32]-NRT-code) [i]
6Linear OOA(2163, 179, F2, 6, 31) (dual of [(179, 6), 911, 32]-NRT-code) [i]
7Linear OOA(2163, 153, F2, 7, 31) (dual of [(153, 7), 908, 32]-NRT-code) [i]
8Linear OOA(2163, 134, F2, 8, 31) (dual of [(134, 8), 909, 32]-NRT-code) [i]