Information on Result #1119452
Linear OOA(3170, 5033631, F3, 5, 10) (dual of [(5033631, 5), 25167985, 11]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(320, 1677877, F3, 5, 3) (dual of [(1677877, 5), 8389365, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, 3713024, F3, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(320, 3713024, F3, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(320, 3713024, F3, 2, 3) (dual of [(3713024, 2), 7426028, 4]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(320, 3713024, F3, 3, 3) (dual of [(3713024, 3), 11139052, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(320, 3713024, F3, 5, 3) (dual of [(3713024, 5), 18565100, 4]-NRT-code), using
- linear OOA(343, 1677877, F3, 5, 5) (dual of [(1677877, 5), 8389342, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- linear OA(343, 4782969, F3, 5) (dual of [4782969, 4782926, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(329, 4782969, F3, 4) (dual of [4782969, 4782940, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(30, 14, F3, 0) (dual of [14, 14, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(343, 4782983, F3, 5) (dual of [4782983, 4782940, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(343, 2391491, F3, 5, 5) (dual of [(2391491, 5), 11957412, 6]-NRT-code), using
- linear OOA(3107, 1677877, F3, 5, 10) (dual of [(1677877, 5), 8389278, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(316, 157, F3, 5, 5) (dual of [(157, 5), 769, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(316, 157, F3, 4, 5) (dual of [(157, 4), 612, 6]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(31, 40, F3, 4, 1) (dual of [(40, 4), 159, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- appending 3 arbitrary columns [i] based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(31, s, F3, 4, 1) for arbitrarily large s, using
- linear OOA(34, 40, F3, 4, 2) (dual of [(40, 4), 156, 3]-NRT-code), using
- appending 2 arbitrary columns [i] based on linear OOA(34, 40, F3, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- appending kth column [i] based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- appending 2 arbitrary columns [i] based on linear OOA(34, 40, F3, 2, 2) (dual of [(40, 2), 76, 3]-NRT-code), using
- linear OOA(311, 77, F3, 4, 5) (dual of [(77, 4), 297, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (6, 11, 77)-net over F3, using
- linear OOA(31, 40, F3, 4, 1) (dual of [(40, 4), 159, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(316, 157, F3, 4, 5) (dual of [(157, 4), 612, 6]-NRT-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
- linear OOA(316, 157, F3, 5, 5) (dual of [(157, 5), 769, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
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(3170, 5033630, F3, 15, 10) (dual of [(5033630, 15), 75504280, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |