Information on Result #1297577

Linear OA(2250, 299, F2, 90) (dual of [299, 49, 91]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2226, 273, F2, 91) (dual of [273, 47, 92]-code), using
    • adding a parity check bit [i] based on linear OA(2225, 272, F2, 90) (dual of [272, 47, 91]-code), using
      • construction XX applied to C1 = C([251,84]), C2 = C([1,86]), C3 = C1 + C2 = C([1,84]), and C∩ = C1 ∩ C2 = C([251,86]) [i] based on
        1. linear OA(2217, 255, F2, 89) (dual of [255, 38, 90]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,84}, and designed minimum distance d ≥ |I|+1 = 90 [i]
        2. linear OA(2210, 255, F2, 86) (dual of [255, 45, 87]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,86], and designed minimum distance d ≥ |I|+1 = 87 [i]
        3. linear OA(2219, 255, F2, 91) (dual of [255, 36, 92]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,86}, and designed minimum distance d ≥ |I|+1 = 92 [i]
        4. linear OA(2208, 255, F2, 84) (dual of [255, 47, 85]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,84], and designed minimum distance d ≥ |I|+1 = 85 [i]
        5. linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
        6. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
  2. linear OA(2226, 275, F2, 74) (dual of [275, 49, 75]-code), using Gilbert–VarÅ¡amov bound and bm = 2226 > Vbs−1(k−1) = 80 712400 004057 050824 588432 549726 142197 733351 164850 011124 137982 745576 [i]
  3. linear OA(222, 24, F2, 15) (dual of [24, 2, 16]-code), using

Mode: 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(2251, 300, F2, 91) (dual of [300, 49, 92]-code) [i]Adding a Parity Check Bit