Information on Result #2226493
Linear OA(2175, 2097201, F2, 16) (dual of [2097201, 2097026, 17]-code), using 1 times truncation based on linear OA(2176, 2097202, F2, 17) (dual of [2097202, 2097026, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 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]
- 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]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(2175, 1048600, F2, 2, 16) (dual of [(1048600, 2), 2097025, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2175, 699067, F2, 3, 16) (dual of [(699067, 3), 2097026, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2175, 524300, F2, 4, 16) (dual of [(524300, 4), 2097025, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2175, 419440, F2, 5, 16) (dual of [(419440, 5), 2097025, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2175, 349533, F2, 6, 16) (dual of [(349533, 6), 2097023, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2175, 299600, F2, 7, 16) (dual of [(299600, 7), 2097025, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(2175, 262150, F2, 8, 16) (dual of [(262150, 8), 2097025, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(2175, 262150, F2, 16, 16) (dual of [(262150, 16), 4194225, 17]-NRT-code) | [i] | OA Folding and Stacking | |