Information on Result #910880

Linear OOA(2200, 106, F2, 2, 107) (dual of [(106, 2), 12, 108]-NRT-code), using concatenation of two NRT-codes based on
  1. linear OA(447, 53, F4, 35) (dual of [53, 6, 36]-code), using
    • construction XX applied to C1 = C([0,101]), C2 = C([1,104]), C3 = C1 + C2 = C([1,101]), and C∩ = C1 ∩ C2 = C([0,104]) [i] based on
      1. linear OA(446, 51, F4, 34) (dual of [51, 5, 35]-code), using contraction [i] based on linear OA(4148, 153, F4, 104) (dual of [153, 5, 105]-code), using the expurgated narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [0,101], and minimum distance d ≥ |{−2,−1,…,101}|+1 = 105 (BCH-bound) [i]
      2. linear OA(446, 51, F4, 34) (dual of [51, 5, 35]-code), using contraction [i] based on linear OA(4148, 153, F4, 104) (dual of [153, 5, 105]-code), using the narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [1,104], and designed minimum distance d ≥ |I|+1 = 105 [i]
      3. linear OA(447, 51, F4, 35) (dual of [51, 4, 36]-code), using contraction [i] based on linear OA(4149, 153, F4, 107) (dual of [153, 4, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [0,104], and minimum distance d ≥ |{−2,−1,…,104}|+1 = 108 (BCH-bound) [i]
      4. linear OA(445, 51, F4, 33) (dual of [51, 6, 34]-code), using contraction [i] based on linear OA(4147, 153, F4, 101) (dual of [153, 6, 102]-code), using the narrow-sense BCH-code C(I) with length 153 | 412−1, defining interval I = [1,101], and designed minimum distance d ≥ |I|+1 = 102 [i]
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
      6. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code) (see above)
  2. linear OOA(22, 2, F2, 2, 2) (dual of [(2, 2), 2, 3]-NRT-code), using

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only
Method
1Linear OOA(2200, 106, F2, 2, 106) (dual of [(106, 2), 12, 107]-NRT-code) [i]Strength Reduction for OOAs
2Linear OOA(2200, 106, F2, 2, 105) (dual of [(106, 2), 12, 106]-NRT-code) [i]
3Linear OOA(2200, 106, F2, 2, 104) (dual of [(106, 2), 12, 105]-NRT-code) [i]