Information on Result #686753
Linear OA(837, 32774, F8, 9) (dual of [32774, 32737, 10]-code), using construction X applied to Ce(8) ⊂ Ce(6) based on
- linear OA(836, 32768, F8, 9) (dual of [32768, 32732, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(831, 32768, F8, 7) (dual of [32768, 32737, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 32767 = 85−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(81, 6, F8, 1) (dual of [6, 5, 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(836, 32773, F8, 8) (dual of [32773, 32737, 9]-code) | [i] | Truncation | |
| 2 | Linear OOA(837, 21292, F8, 2, 9) (dual of [(21292, 2), 42547, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(837, 21292, F8, 3, 9) (dual of [(21292, 3), 63839, 10]-NRT-code) | [i] | ||
| 4 | Digital (28, 37, 21292)-net over F8 | [i] | ||
| 5 | Linear OOA(837, 16387, F8, 2, 9) (dual of [(16387, 2), 32737, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(837, 10924, F8, 3, 9) (dual of [(10924, 3), 32735, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(837, 8193, F8, 9, 9) (dual of [(8193, 9), 73700, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |