Information on Result #1297209

Linear OA(283, 8211, F2, 12) (dual of [8211, 8128, 13]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(279, 8206, F2, 12) (dual of [8206, 8127, 13]-code), using
    • 1 times truncation [i] based on linear OA(280, 8207, F2, 13) (dual of [8207, 8127, 14]-code), using
      • construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
        1. linear OA(279, 8192, F2, 13) (dual of [8192, 8113, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
        2. linear OA(266, 8192, F2, 11) (dual of [8192, 8126, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
        3. linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
        4. linear OA(21, 15, F2, 1) (dual of [15, 14, 2]-code), using
  2. linear OA(279, 8207, F2, 8) (dual of [8207, 8128, 9]-code), using Gilbert–VarÅ¡amov bound and bm = 279 > Vbs−1(k−1) = 496305 635124 147541 989044 [i]
  3. linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), 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(284, 8212, F2, 13) (dual of [8212, 8128, 14]-code) [i]Adding a Parity Check Bit
2Linear OOA(283, 2737, F2, 3, 12) (dual of [(2737, 3), 8128, 13]-NRT-code) [i]OOA Folding