Information on Result #701709

Linear OA(263, 280, F2, 15) (dual of [280, 217, 16]-code), using construction XX applied to C1 = C([251,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([251,10]) based on
  1. linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,8}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  2. linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
  3. linear OA(257, 255, F2, 15) (dual of [255, 198, 16]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,10}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  4. linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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(262, 279, F2, 14) (dual of [279, 217, 15]-code) [i]Truncation
2Linear OOA(263, 140, F2, 2, 15) (dual of [(140, 2), 217, 16]-NRT-code) [i]OOA Folding
3Linear OOA(263, 93, F2, 3, 15) (dual of [(93, 3), 216, 16]-NRT-code) [i]
4Linear OOA(263, 70, F2, 4, 15) (dual of [(70, 4), 217, 16]-NRT-code) [i]
5Linear OOA(263, 56, F2, 5, 15) (dual of [(56, 5), 217, 16]-NRT-code) [i]