Information on Result #1445314
Linear OOA(8114, 4106, F8, 2, 32) (dual of [(4106, 2), 8098, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(8114, 4106, F8, 32) (dual of [4106, 3992, 33]-code), using
- 5 step Varšamov–Edel lengthening with (ri) = (1, 4 times 0) [i] based on linear OA(8113, 4100, F8, 32) (dual of [4100, 3987, 33]-code), using
- 1 times truncation [i] 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
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(8114, 4101, F8, 33) (dual of [4101, 3987, 34]-code), using
Mode: 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(8114, 2053, F8, 3, 32) (dual of [(2053, 3), 6045, 33]-NRT-code) | [i] | OOA Folding | |