Information on Result #1018852
Linear OOA(8149, 2305, F81, 3, 19) (dual of [(2305, 3), 6866, 20]-NRT-code), using (u, u+v)-construction based on
- linear OOA(8111, 116, F81, 3, 9) (dual of [(116, 3), 337, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,338P) [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- linear OOA(8138, 2189, F81, 3, 19) (dual of [(2189, 3), 6529, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), using
- construction X applied to C([0,9]) ⊂ C([0,8]) [i] based on
- linear OA(8137, 6562, F81, 19) (dual of [6562, 6525, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(8133, 6562, F81, 17) (dual of [6562, 6529, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 6562 | 814−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,9]) ⊂ C([0,8]) [i] based on
- OOA 3-folding [i] based on linear OA(8138, 6567, F81, 19) (dual of [6567, 6529, 20]-code), 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(8149, 768, F81, 21, 19) (dual of [(768, 21), 16079, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |