Information on Result #1020176

Linear OOA(25667, 2818050, F256, 3, 17) (dual of [(2818050, 3), 8454083, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(25618, 21849, F256, 3, 8) (dual of [(21849, 3), 65529, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(25618, 65547, F256, 8) (dual of [65547, 65529, 9]-code), using
      • construction X applied to Ce(7) ⊂ Ce(3) [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(2567, 65536, F256, 4) (dual of [65536, 65529, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(2563, 11, F256, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,256) or 11-cap in PG(2,256)), 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(25667, 1409025, F256, 6, 17) (dual of [(1409025, 6), 8454083, 18]-NRT-code) [i]OOA Folding