Information on Result #687198
Linear OA(830, 4101, F8, 9) (dual of [4101, 4071, 10]-code), using construction X applied to Ce(8) ⊂ Ce(6) based on
- 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(825, 4096, F8, 7) (dual of [4096, 4071, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(81, 5, F8, 1) (dual of [5, 4, 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(829, 4100, F8, 8) (dual of [4100, 4071, 9]-code) | [i] | Truncation | |
| 2 | Linear OOA(830, 2658, F8, 2, 9) (dual of [(2658, 2), 5286, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(830, 2658, F8, 3, 9) (dual of [(2658, 3), 7944, 10]-NRT-code) | [i] | ||
| 4 | Digital (21, 30, 2658)-net over F8 | [i] | ||
| 5 | Linear OOA(830, 2050, F8, 2, 9) (dual of [(2050, 2), 4070, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(830, 1367, F8, 3, 9) (dual of [(1367, 3), 4071, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(830, 1025, F8, 9, 9) (dual of [(1025, 9), 9195, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |