Information on Result #629396

Linear OA(2161, 177, F2, 75) (dual of [177, 16, 76]-code), using concatenation of two codes based on
  1. linear OA(451, 59, F4, 37) (dual of [59, 8, 38]-code), using
    • 6 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
  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(2161, 177, F2, 74) (dual of [177, 16, 75]-code) [i]Strength Reduction
2Linear OA(2161, 177, F2, 73) (dual of [177, 16, 74]-code) [i]
3Linear OA(2161, 177, F2, 72) (dual of [177, 16, 73]-code) [i]
4Linear OA(2161, 177, F2, 71) (dual of [177, 16, 72]-code) [i]
5Linear OA(2161, 177, F2, 70) (dual of [177, 16, 71]-code) [i]
6Linear OA(2161, 177, F2, 69) (dual of [177, 16, 70]-code) [i]
7Linear OA(2160, 176, F2, 74) (dual of [176, 16, 75]-code) [i]Truncation
8Linear OA(2159, 175, F2, 73) (dual of [175, 16, 74]-code) [i]
9Linear OA(2157, 173, F2, 71) (dual of [173, 16, 72]-code) [i]
10Linear OA(2156, 172, F2, 70) (dual of [172, 16, 71]-code) [i]
11Linear OOA(2161, 88, F2, 2, 75) (dual of [(88, 2), 15, 76]-NRT-code) [i]OOA Folding
12Linear OOA(2161, 59, F2, 3, 75) (dual of [(59, 3), 16, 76]-NRT-code) [i]
13Linear OOA(2161, 35, F2, 5, 75) (dual of [(35, 5), 14, 76]-NRT-code) [i]