Information on Result #2226362
Linear OA(2169, 2097174, F2, 16) (dual of [2097174, 2097005, 17]-code), using 1 times truncation based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2169, 2097152, F2, 17) (dual of [2097152, 2096983, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, 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 OA(2171, 2097176, F2, 16) (dual of [2097176, 2097005, 17]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2172, 2097177, F2, 16) (dual of [2097177, 2097005, 17]-code) | [i] | ||
| 3 | Linear OA(2173, 2097178, F2, 16) (dual of [2097178, 2097005, 17]-code) | [i] | ||
| 4 | Linear OOA(2169, 1048587, F2, 2, 16) (dual of [(1048587, 2), 2097005, 17]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2169, 699058, F2, 3, 16) (dual of [(699058, 3), 2097005, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2169, 524293, F2, 4, 16) (dual of [(524293, 4), 2097003, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(2169, 419434, F2, 5, 16) (dual of [(419434, 5), 2097001, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(2169, 349529, F2, 6, 16) (dual of [(349529, 6), 2097005, 17]-NRT-code) | [i] | ||
| 9 | Linear OOA(2169, 299596, F2, 7, 16) (dual of [(299596, 7), 2097003, 17]-NRT-code) | [i] | ||
| 10 | Linear OOA(2169, 262146, F2, 8, 16) (dual of [(262146, 8), 2096999, 17]-NRT-code) | [i] | ||
| 11 | Linear OOA(2169, 262146, F2, 16, 16) (dual of [(262146, 16), 4194167, 17]-NRT-code) | [i] | OA Folding and Stacking | |