Information on Result #1016164

Linear OOA(9135, 7186730, F9, 3, 13) (dual of [(7186730, 3), 21560055, 14]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(937, 1594328, F9, 3, 6) (dual of [(1594328, 3), 4782947, 7]-NRT-code), using
    • OOA 3-folding [i] based on linear OA(937, 4782984, F9, 6) (dual of [4782984, 4782947, 7]-code), using
      • construction X applied to Ce(5) ⊂ Ce(3) [i] based on
        1. linear OA(936, 4782969, F9, 6) (dual of [4782969, 4782933, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(922, 4782969, F9, 4) (dual of [4782969, 4782947, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
        3. linear OA(91, 15, F9, 1) (dual of [15, 14, 2]-code), using
  2. linear OOA(998, 5592402, F9, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
    • trace code [i] based on linear OOA(8149, 2796201, F81, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
      • OOA 3-folding [i] based on linear OA(8149, large, F81, 13) (dual of [large, large−49, 14]-code), using
        • the expurgated narrow-sense BCH-code C(I) with length 21523361 | 818−1, 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(9136, 7186730, F9, 3, 13) (dual of [(7186730, 3), 21560054, 14]-NRT-code) [i]OOA Duplication
2Linear OOA(9135, 3593364, F9, 15, 13) (dual of [(3593364, 15), 53900325, 14]-NRT-code) [i]OOA Folding and Stacking with Additional Row