Information on Result #731712

Linear OA(2147, 159, F2, 71) (dual of [159, 12, 72]-code), using concatenation of two 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 OA(21, 3, F2, 1) (dual of [3, 2, 2]-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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2147, 159, F2, 70) (dual of [159, 12, 71]-code) [i]Strength Reduction
2Linear OA(2148, 160, F2, 71) (dual of [160, 12, 72]-code) [i]Code Embedding in Larger Space
3Linear OA(2149, 161, F2, 71) (dual of [161, 12, 72]-code) [i]
4Linear OA(2146, 158, F2, 70) (dual of [158, 12, 71]-code) [i]Truncation
5Linear OA(2145, 157, F2, 69) (dual of [157, 12, 70]-code) [i]
6Linear OOA(2147, 53, F2, 3, 71) (dual of [(53, 3), 12, 72]-NRT-code) [i]OOA Folding