Information on Result #1297441

Linear OA(2221, 269, F2, 82) (dual of [269, 48, 83]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2206, 253, F2, 82) (dual of [253, 47, 83]-code), using
    • 3 times truncation [i] based on 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]
  2. linear OA(2206, 254, F2, 67) (dual of [254, 48, 68]-code), using Gilbert–VarÅ¡amov bound and bm = 2206 > Vbs−1(k−1) = 101 555339 624305 135175 396878 158663 330446 568776 201831 862927 134548 [i]
  3. linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), 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(2221, 269, F2, 81) (dual of [269, 48, 82]-code) [i]Strength Reduction
2Linear OA(2221, 269, F2, 80) (dual of [269, 48, 81]-code) [i]
3Linear OA(2222, 270, F2, 83) (dual of [270, 48, 84]-code) [i]Adding a Parity Check Bit