Information on Result #2226642
Linear OA(2218, 540, F2, 50) (dual of [540, 322, 51]-code), using 1 times truncation based on linear OA(2219, 541, F2, 51) (dual of [541, 322, 52]-code), using
- construction X applied to Ce(50) ⊂ Ce(44) [i] based on
- linear OA(2208, 512, F2, 51) (dual of [512, 304, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2190, 512, F2, 45) (dual of [512, 322, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(211, 29, F2, 5) (dual of [29, 18, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using
- an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2220, 542, F2, 50) (dual of [542, 322, 51]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2237, 583, F2, 50) (dual of [583, 346, 51]-code) | [i] | Varšamov–Edel Lengthening | |
| 3 | Linear OA(2238, 588, F2, 50) (dual of [588, 350, 51]-code) | [i] | ||
| 4 | Linear OA(2239, 594, F2, 50) (dual of [594, 355, 51]-code) | [i] | ||
| 5 | Linear OOA(2218, 270, F2, 2, 50) (dual of [(270, 2), 322, 51]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2218, 180, F2, 3, 50) (dual of [(180, 3), 322, 51]-NRT-code) | [i] | ||
| 7 | Linear OOA(2218, 135, F2, 4, 50) (dual of [(135, 4), 322, 51]-NRT-code) | [i] | ||
| 8 | Linear OOA(2218, 108, F2, 5, 50) (dual of [(108, 5), 322, 51]-NRT-code) | [i] | ||