Information on Result #674181
Linear OA(233, 78, F2, 11) (dual of [78, 45, 12]-code), using construction X applied to Ce(10) ⊂ Ce(6) based on
- linear OA(228, 64, F2, 11) (dual of [64, 36, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(219, 64, F2, 7) (dual of [64, 45, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25, 14, F2, 3) (dual of [14, 9, 4]-code or 14-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), 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.
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(233, 78, F2, 10) (dual of [78, 45, 11]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(234, 79, F2, 11) (dual of [79, 45, 12]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(232, 77, F2, 10) (dual of [77, 45, 11]-code) | [i] | Truncation | |
| 4 | Linear OA(2240, 589, F2, 50) (dual of [589, 349, 51]-code) | [i] | Construction X with Cyclic Codes | |
| 5 | Linear OA(2249, 589, F2, 52) (dual of [589, 340, 53]-code) | [i] | ||
| 6 | Linear OA(2258, 589, F2, 54) (dual of [589, 331, 55]-code) | [i] | ||
| 7 | Linear OOA(233, 39, F2, 2, 11) (dual of [(39, 2), 45, 12]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(233, 26, F2, 3, 11) (dual of [(26, 3), 45, 12]-NRT-code) | [i] | ||