Information on Result #701852

Linear OA(2124, 287, F2, 30) (dual of [287, 163, 31]-code), using construction XX applied to C1 = C([251,24]), C2 = C([1,26]), C3 = C1 + C2 = C([1,24]), and C∩ = C1 ∩ C2 = C([251,26]) based on
  1. linear OA(2109, 255, F2, 29) (dual of [255, 146, 30]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  2. linear OA(2100, 255, F2, 26) (dual of [255, 155, 27]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
  3. linear OA(2117, 255, F2, 31) (dual of [255, 138, 32]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,26}, and designed minimum distance d ≥ |I|+1 = 32 [i]
  4. linear OA(292, 255, F2, 24) (dual of [255, 163, 25]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
  5. linear OA(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
  6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-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 OA(2126, 289, F2, 30) (dual of [289, 163, 31]-code) [i]Code Embedding in Larger Space
2Linear OA(2125, 288, F2, 31) (dual of [288, 163, 32]-code) [i]Adding a Parity Check Bit
3Linear OOA(2124, 143, F2, 2, 30) (dual of [(143, 2), 162, 31]-NRT-code) [i]OOA Folding