Information on Result #1297485

Linear OA(2229, 277, F2, 86) (dual of [277, 48, 87]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2211, 258, F2, 86) (dual of [258, 47, 87]-code), using
    • 1 times truncation [i] based on linear OA(2212, 259, F2, 87) (dual of [259, 47, 88]-code), using
      • construction X applied to Ce(86) ⊂ Ce(84) [i] based on
        1. linear OA(2211, 256, F2, 87) (dual of [256, 45, 88]-code), using an extension Ce(86) of 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]
        2. linear OA(2209, 256, F2, 85) (dual of [256, 47, 86]-code), using an extension Ce(84) of 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]
        3. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-code), using
  2. linear OA(2211, 259, F2, 68) (dual of [259, 48, 69]-code), using Gilbert–VarÅ¡amov bound and bm = 2211 > Vbs−1(k−1) = 1288 439491 289880 083651 028009 614516 457982 306386 781906 313688 090836 [i]
  3. linear OA(217, 18, F2, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,2)), 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(2229, 277, F2, 85) (dual of [277, 48, 86]-code) [i]Strength Reduction
2Linear OA(2231, 279, F2, 86) (dual of [279, 48, 87]-code) [i]Code Embedding in Larger Space
3Linear OA(2232, 280, F2, 86) (dual of [280, 48, 87]-code) [i]
4Linear OA(2230, 278, F2, 87) (dual of [278, 48, 88]-code) [i]Adding a Parity Check Bit