Information on Result #731206
Linear OA(8118, 524302, F8, 20) (dual of [524302, 524184, 21]-code), using trace code based on linear OA(6459, 262151, F64, 20) (dual of [262151, 262092, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(17) [i] based on
- linear OA(6458, 262144, F64, 20) (dual of [262144, 262086, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(6452, 262144, F64, 18) (dual of [262144, 262092, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 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(8119, 524303, F8, 20) (dual of [524303, 524184, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(8118, 524302, F8, 2, 20) (dual of [(524302, 2), 1048486, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8118, 524302, F8, 3, 20) (dual of [(524302, 3), 1572788, 21]-NRT-code) | [i] | ||
| 4 | Digital (98, 118, 524302)-net over F8 | [i] | ||
| 5 | Linear OA(8119, 524304, F8, 20) (dual of [524304, 524185, 21]-code) | [i] | Construction X with Varšamov Bound | |
| 6 | Linear OOA(8118, 262151, F8, 2, 20) (dual of [(262151, 2), 524184, 21]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(8118, 174767, F8, 3, 20) (dual of [(174767, 3), 524183, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(8118, 52430, F8, 20, 20) (dual of [(52430, 20), 1048482, 21]-NRT-code) | [i] | OA Folding and Stacking | |