Information on Result #895034

Linear OOA(3141, 4194427, F3, 2, 12) (dual of [(4194427, 2), 8388713, 13]-NRT-code), using (u, u+v)-construction based on
  1. linear OOA(321, 126, F3, 2, 6) (dual of [(126, 2), 231, 7]-NRT-code), using
    • OOA 2-folding [i] based on linear OA(321, 252, F3, 6) (dual of [252, 231, 7]-code), using
      • construction XX applied to C1 = C([241,3]), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C([241,4]) [i] based on
        1. linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,1,2,3}, and designed minimum distance d ≥ |I|+1 = 6 [i]
        2. linear OA(316, 242, F3, 5) (dual of [242, 226, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
        3. linear OA(321, 242, F3, 6) (dual of [242, 221, 7]-code), using the primitive BCH-code C(I) with length 242 = 35−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
        4. linear OA(311, 242, F3, 4) (dual of [242, 231, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [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(3120, 4194301, F3, 2, 12) (dual of [(4194301, 2), 8388482, 13]-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(3141, 2097213, F3, 4, 12) (dual of [(2097213, 4), 8388711, 13]-NRT-code) [i]OOA Folding