Information on Result #2251696
Linear OA(8113, 4100, F8, 32) (dual of [4100, 3987, 33]-code), using 1 times truncation based on linear OA(8114, 4101, F8, 33) (dual of [4101, 3987, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- linear OA(8113, 4096, F8, 33) (dual of [4096, 3983, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(8109, 4096, F8, 31) (dual of [4096, 3987, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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 OOA(8113, 4030, F8, 2, 32) (dual of [(4030, 2), 7947, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(8113, 4030, F8, 3, 32) (dual of [(4030, 3), 11977, 33]-NRT-code) | [i] | ||
| 3 | Digital (81, 113, 4030)-net over F8 | [i] | ||
| 4 | Linear OA(8114, 4106, F8, 32) (dual of [4106, 3992, 33]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OOA(8113, 2050, F8, 2, 32) (dual of [(2050, 2), 3987, 33]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8113, 1366, F8, 3, 32) (dual of [(1366, 3), 3985, 33]-NRT-code) | [i] | ||