Information on Result #701707

Linear OA(251, 273, F2, 13) (dual of [273, 222, 14]-code), using construction XX applied to C1 = C([253,8]), C2 = C([0,10]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([253,10]) based on
  1. linear OA(241, 255, F2, 11) (dual of [255, 214, 12]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [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(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 = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [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(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
  6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code) (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(250, 272, F2, 12) (dual of [272, 222, 13]-code) [i]Truncation
2Linear OOA(251, 136, F2, 2, 13) (dual of [(136, 2), 221, 14]-NRT-code) [i]OOA Folding
3Linear OOA(251, 91, F2, 3, 13) (dual of [(91, 3), 222, 14]-NRT-code) [i]
4Linear OOA(251, 68, F2, 4, 13) (dual of [(68, 4), 221, 14]-NRT-code) [i]
5Linear OOA(251, 54, F2, 5, 13) (dual of [(54, 5), 219, 14]-NRT-code) [i]
6Linear OOA(251, 45, F2, 6, 13) (dual of [(45, 6), 219, 14]-NRT-code) [i]