Information on Result #701718

Linear OA(259, 273, F2, 15) (dual of [273, 214, 16]-code), using construction XX applied to C1 = C([253,10]), C2 = C([0,12]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([253,12]) 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 = {−2,−1,…,10}, and designed minimum distance d ≥ |I|+1 = 14 [i]
  2. linear OA(249, 255, F2, 13) (dual of [255, 206, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [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 = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
  4. 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]
  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(258, 272, F2, 14) (dual of [272, 214, 15]-code) [i]Truncation
2Linear OOA(259, 136, F2, 2, 15) (dual of [(136, 2), 213, 16]-NRT-code) [i]OOA Folding
3Linear OOA(259, 91, F2, 3, 15) (dual of [(91, 3), 214, 16]-NRT-code) [i]
4Linear OOA(259, 68, F2, 4, 15) (dual of [(68, 4), 213, 16]-NRT-code) [i]
5Linear OOA(259, 54, F2, 5, 15) (dual of [(54, 5), 211, 16]-NRT-code) [i]
6Linear OOA(259, 45, F2, 6, 15) (dual of [(45, 6), 211, 16]-NRT-code) [i]