Information on Result #1010667

Linear OOA(3175, 3327651, F3, 3, 13) (dual of [(3327651, 3), 9982778, 14]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(354, 531450, F3, 3, 6) (dual of [(531450, 3), 1594296, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(354, 1594350, F3, 6) (dual of [1594350, 1594296, 7]-code), using
      • construction X applied to Ce(6) ⊂ Ce(3) [i] based on
        1. linear OA(353, 1594323, F3, 7) (dual of [1594323, 1594270, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
        2. linear OA(327, 1594323, F3, 4) (dual of [1594323, 1594296, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(31, 27, F3, 1) (dual of [27, 26, 2]-code), using
  2. linear OOA(3121, 2796201, F3, 3, 13) (dual of [(2796201, 3), 8388482, 14]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(3121, large, F3, 13) (dual of [large, large−121, 14]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (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(3176, 3327651, F3, 3, 13) (dual of [(3327651, 3), 9982777, 14]-NRT-code) [i]OOA Duplication