Information on Result #1613525
Linear OOA(8147, 2189, F81, 4, 23) (dual of [(2189, 4), 8709, 24]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(8147, 2189, F81, 3, 23) (dual of [(2189, 3), 6520, 24]-NRT-code), using
- 811 times duplication [i] based on linear OOA(8146, 2189, F81, 3, 23) (dual of [(2189, 3), 6521, 24]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8146, 6567, F81, 23) (dual of [6567, 6521, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(8145, 6562, F81, 23) (dual of [6562, 6517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(8141, 6562, F81, 21) (dual of [6562, 6521, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(811, 5, F81, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(811, s, F81, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- OOA 3-folding [i] based on linear OA(8146, 6567, F81, 23) (dual of [6567, 6521, 24]-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(8147, 729, F81, 28, 23) (dual of [(729, 28), 20365, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |