Information on Result #1009443

Linear OOA(2226, 2796546, F2, 3, 17) (dual of [(2796546, 3), 8389412, 18]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(241, 345, F2, 3, 8) (dual of [(345, 3), 994, 9]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(241, 1035, F2, 8) (dual of [1035, 994, 9]-code), using
      • 1 times truncation [i] based on linear OA(242, 1036, F2, 9) (dual of [1036, 994, 10]-code), using
        • construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
          1. linear OA(241, 1024, F2, 9) (dual of [1024, 983, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
          2. linear OA(231, 1024, F2, 7) (dual of [1024, 993, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
          3. linear OA(211, 12, F2, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,2)), using
          4. linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
  2. linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [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(2226, 1398273, F2, 6, 17) (dual of [(1398273, 6), 8389412, 18]-NRT-code) [i]OOA Folding