Information on Result #1010719

Linear OOA(3166, 2796933, F3, 3, 14) (dual of [(2796933, 3), 8390633, 15]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(330, 732, F3, 3, 7) (dual of [(732, 3), 2166, 8]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(330, 2196, F3, 7) (dual of [2196, 2166, 8]-code), using
      • construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
        1. linear OA(329, 2187, F3, 7) (dual of [2187, 2158, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
        3. linear OA(38, 9, F3, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
        4. linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
  2. linear OOA(3136, 2796201, F3, 3, 14) (dual of [(2796201, 3), 8388467, 15]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
      • the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [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(3167, 2796933, F3, 3, 14) (dual of [(2796933, 3), 8390632, 15]-NRT-code) [i]OOA Duplication