Information on Result #1020174

Linear OOA(25665, 2818048, F256, 3, 17) (dual of [(2818048, 3), 8454079, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25616, 21847, F256, 3, 8) (dual of [(21847, 3), 65525, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25616, 65541, F256, 8) (dual of [65541, 65525, 9]-code), using
      • construction X applied to Ce(7) ⊂ Ce(5) [i] based on
        1. linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
        2. linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
  2. linear OOA(25649, 2796201, F256, 3, 17) (dual of [(2796201, 3), 8388554, 18]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25649, large, F256, 17) (dual of [large, large−49, 18]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(25665, 1409024, F256, 6, 17) (dual of [(1409024, 6), 8454079, 18]-NRT-code) [i]OOA Folding