Information on Result #895236

Linear OOA(3211, 4194427, F3, 2, 18) (dual of [(4194427, 2), 8388643, 19]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(331, 126, F3, 2, 9) (dual of [(126, 2), 221, 10]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(331, 252, F3, 9) (dual of [252, 221, 10]-code), using
      • construction XX applied to C1 = C([241,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([241,7]) [i] based on
        1. linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
        2. linear OA(326, 242, F3, 8) (dual of [242, 216, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
        3. linear OA(331, 242, F3, 9) (dual of [242, 211, 10]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [i]
        4. linear OA(321, 242, F3, 7) (dual of [242, 221, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
        5. linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code), using
        6. linear OA(30, 5, F3, 0) (dual of [5, 5, 1]-code) (see above)
  2. linear OOA(3180, 4194301, F3, 2, 18) (dual of [(4194301, 2), 8388422, 19]-NRT-code), using

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(3211, 2097213, F3, 4, 18) (dual of [(2097213, 4), 8388641, 19]-NRT-code) [i]OOA Folding