Information on Result #1117103
Linear OOA(3114, 1678817, F3, 5, 10) (dual of [(1678817, 5), 8393971, 11]-NRT-code), using (u, u+v)-construction based on
- linear OOA(323, 1097, F3, 5, 5) (dual of [(1097, 5), 5462, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(323, 2195, F3, 5) (dual of [2195, 2172, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(323, 2196, F3, 5) (dual of [2196, 2173, 6]-code), using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(322, 2187, F3, 5) (dual of [2187, 2165, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(315, 2187, F3, 4) (dual of [2187, 2172, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(38, 9, F3, 8) (dual of [9, 1, 9]-code or 9-arc in PG(7,3)), using
- dual of repetition code with length 9 [i]
- linear OA(31, 9, F3, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to Ce(4) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(323, 2196, F3, 5) (dual of [2196, 2173, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(323, 2195, F3, 5) (dual of [2195, 2172, 6]-code), using
- linear OOA(391, 1677720, F3, 5, 10) (dual of [(1677720, 5), 8388509, 11]-NRT-code), using
- OOA 5-folding [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- OOA 5-folding [i] based on linear OA(391, 8388600, F3, 10) (dual of [8388600, 8388509, 11]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3114, 1678816, F3, 15, 10) (dual of [(1678816, 15), 25182126, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |