Information on Result #701815

Linear OA(2107, 280, F2, 27) (dual of [280, 173, 28]-code), using construction XX applied to C1 = C([251,20]), C2 = C([0,22]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([251,22]) based on
  1. linear OA(293, 255, F2, 25) (dual of [255, 162, 26]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
  2. linear OA(285, 255, F2, 23) (dual of [255, 170, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
  3. linear OA(2101, 255, F2, 27) (dual of [255, 154, 28]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,22}, and designed minimum distance d ≥ |I|+1 = 28 [i]
  4. linear OA(277, 255, F2, 21) (dual of [255, 178, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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(2106, 279, F2, 26) (dual of [279, 173, 27]-code) [i]Truncation
2Linear OOA(2107, 140, F2, 2, 27) (dual of [(140, 2), 173, 28]-NRT-code) [i]OOA Folding
3Linear OOA(2107, 93, F2, 3, 27) (dual of [(93, 3), 172, 28]-NRT-code) [i]
4Linear OOA(2107, 70, F2, 4, 27) (dual of [(70, 4), 173, 28]-NRT-code) [i]
5Linear OOA(2107, 56, F2, 5, 27) (dual of [(56, 5), 173, 28]-NRT-code) [i]