Information on Result #702162

Linear OA(2236, 579, F2, 50) (dual of [579, 343, 51]-code), using construction X applied to C([1,50]) ⊂ C([1,38]) based on
  1. linear OA(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
  2. linear OA(2162, 511, F2, 38) (dual of [511, 349, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
  3. linear OA(229, 68, F2, 11) (dual of [68, 39, 12]-code), using
    • construction X applied to Ce(10) ⊂ Ce(8) [i] based on
      1. linear OA(228, 64, F2, 11) (dual of [64, 36, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
      2. linear OA(225, 64, F2, 9) (dual of [64, 39, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
      3. linear OA(21, 4, F2, 1) (dual of [4, 3, 2]-code), using

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(2237, 580, F2, 51) (dual of [580, 343, 52]-code) [i]Adding a Parity Check Bit
2Linear OOA(2236, 289, F2, 2, 50) (dual of [(289, 2), 342, 51]-NRT-code) [i]OOA Folding
3Linear OOA(2236, 193, F2, 3, 50) (dual of [(193, 3), 343, 51]-NRT-code) [i]