Information on Result #1084663
Linear OOA(3205, 4194341, F3, 4, 14) (dual of [(4194341, 4), 16777159, 15]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(38, 41, F3, 4, 4) (dual of [(41, 4), 156, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(38, 41, F3, 3, 4) (dual of [(41, 3), 115, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 41)-net over F3, using
- appending kth column [i] based on linear OOA(38, 41, F3, 3, 4) (dual of [(41, 3), 115, 5]-NRT-code), using
- linear OOA(361, 2097150, F3, 4, 7) (dual of [(2097150, 4), 8388539, 8]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(361, 2796200, F3, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(361, 8388601, F3, 7) (dual of [8388601, 8388540, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 330−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(361, large, F3, 7) (dual of [large, large−61, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(361, 8388601, F3, 7) (dual of [8388601, 8388540, 8]-code), using
- discarding factors / shortening the dual code based on linear OOA(361, 2796200, F3, 4, 7) (dual of [(2796200, 4), 11184739, 8]-NRT-code), using
- linear OOA(3136, 2097150, F3, 4, 14) (dual of [(2097150, 4), 8388464, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3136, large, F3, 14) (dual of [large, large−136, 15]-code), using
- OOA 4-folding [i] based on linear OA(3136, 8388600, F3, 14) (dual of [8388600, 8388464, 15]-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(3205, 2097170, F3, 20, 14) (dual of [(2097170, 20), 41943195, 15]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |