Information on Result #701753

Linear OA(292, 283, F2, 22) (dual of [283, 191, 23]-code), using construction XX applied to C1 = C([251,16]), C2 = C([1,18]), C3 = C1 + C2 = C([1,16]), and C∩ = C1 ∩ C2 = C([251,18]) based on
  1. linear OA(281, 255, F2, 21) (dual of [255, 174, 22]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
  2. linear OA(268, 255, F2, 18) (dual of [255, 187, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
  3. linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,18}, and designed minimum distance d ≥ |I|+1 = 24 [i]
  4. linear OA(264, 255, F2, 16) (dual of [255, 191, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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, 5, F2, 1) (dual of [5, 4, 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(294, 285, F2, 22) (dual of [285, 191, 23]-code) [i]Code Embedding in Larger Space
2Linear OA(293, 284, F2, 23) (dual of [284, 191, 24]-code) [i]Adding a Parity Check Bit
3Linear OOA(292, 141, F2, 2, 22) (dual of [(141, 2), 190, 23]-NRT-code) [i]OOA Folding
4Linear OOA(292, 94, F2, 3, 22) (dual of [(94, 3), 190, 23]-NRT-code) [i]