Information on Result #687241
Linear OA(838, 4105, F8, 11) (dual of [4105, 4067, 12]-code), using construction X applied to Ce(10) ⊂ Ce(8) based on
- linear OA(837, 4096, F8, 11) (dual of [4096, 4059, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(81, 9, F8, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(81, s, F8, 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(839, 4106, F8, 11) (dual of [4106, 4067, 12]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(838, 3053, F8, 2, 11) (dual of [(3053, 2), 6068, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(838, 3053, F8, 3, 11) (dual of [(3053, 3), 9121, 12]-NRT-code) | [i] | ||
| 4 | Digital (27, 38, 3053)-net over F8 | [i] | ||
| 5 | Linear OOA(838, 2052, F8, 2, 11) (dual of [(2052, 2), 4066, 12]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(838, 1368, F8, 3, 11) (dual of [(1368, 3), 4066, 12]-NRT-code) | [i] | ||
| 7 | Linear OOA(838, 820, F8, 11, 11) (dual of [(820, 11), 8982, 12]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |