Information on Result #672215

Linear OA(2176, 2097202, F2, 17) (dual of [2097202, 2097026, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
  1. linear OA(2169, 2097153, F2, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
  2. linear OA(2127, 2097153, F2, 13) (dual of [2097153, 2097026, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
  3. linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), 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 OA(2175, 2097201, F2, 16) (dual of [2097201, 2097026, 17]-code) [i]Truncation
2Linear OOA(2176, 1048601, F2, 2, 17) (dual of [(1048601, 2), 2097026, 18]-NRT-code) [i]OOA Folding
3Linear OOA(2176, 699067, F2, 3, 17) (dual of [(699067, 3), 2097025, 18]-NRT-code) [i]
4Linear OOA(2176, 524300, F2, 4, 17) (dual of [(524300, 4), 2097024, 18]-NRT-code) [i]
5Linear OOA(2176, 419440, F2, 5, 17) (dual of [(419440, 5), 2097024, 18]-NRT-code) [i]
6Linear OOA(2176, 349533, F2, 6, 17) (dual of [(349533, 6), 2097022, 18]-NRT-code) [i]
7Linear OOA(2176, 299600, F2, 7, 17) (dual of [(299600, 7), 2097024, 18]-NRT-code) [i]
8Linear OOA(2176, 262150, F2, 8, 17) (dual of [(262150, 8), 2097024, 18]-NRT-code) [i]
9Linear OOA(2176, 262150, F2, 17, 17) (dual of [(262150, 17), 4456374, 18]-NRT-code) [i]OOA Folding and Stacking with Additional Row