Information on Result #1013492
Linear OOA(5139, 5233, F5, 3, 25) (dual of [(5233, 3), 15560, 26]-NRT-code), using (u, u+v)-construction based on
- linear OOA(517, 20, F5, 3, 12) (dual of [(20, 3), 43, 13]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(3;F,47P) [i] based on function field F/F5 with g(F) = 5 and N(F) ≥ 20, using
- linear OOA(5122, 5213, F5, 3, 25) (dual of [(5213, 3), 15517, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(5122, 15639, F5, 25) (dual of [15639, 15517, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(5121, 15626, F5, 25) (dual of [15626, 15505, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(5109, 15626, F5, 23) (dual of [15626, 15517, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 512−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(51, 13, F5, 1) (dual of [13, 12, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- OOA 3-folding [i] based on linear OA(5122, 15639, F5, 25) (dual of [15639, 15517, 26]-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(5139, 1308, F5, 27, 25) (dual of [(1308, 27), 35177, 26]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |