Information on Result #1017326
Linear OOA(4944, 39269, F49, 3, 13) (dual of [(39269, 3), 117763, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(496, 50, F49, 3, 6) (dual of [(50, 3), 144, 7]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;144,49) [i]
- linear OOA(4938, 39219, F49, 3, 13) (dual of [(39219, 3), 117619, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- linear OA(4937, 117650, F49, 13) (dual of [117650, 117613, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(4931, 117650, F49, 11) (dual of [117650, 117619, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 117650 | 496−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(491, 7, F49, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,6]) ⊂ C([0,5]) [i] based on
- OOA 3-folding [i] based on linear OA(4938, 117657, F49, 13) (dual of [117657, 117619, 14]-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(4944, 19634, F49, 15, 13) (dual of [(19634, 15), 294466, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |