Information on Result #1119455
Linear OOA(3193, 7579183, F3, 5, 10) (dual of [(7579183, 5), 37895722, 11]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(320, 2391491, F3, 5, 3) (dual of [(2391491, 5), 11957435, 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, 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
- linear OOA(3130, 2796201, F3, 5, 10) (dual of [(2796201, 5), 13980875, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3130, 5592402, F3, 3, 10) (dual of [(5592402, 3), 16777076, 11]-NRT-code), using
- trace code [i] based on linear OOA(965, 2796201, F9, 3, 10) (dual of [(2796201, 3), 8388538, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 3-folding [i] based on linear OA(965, large, F9, 10) (dual of [large, large−65, 11]-code), using
- trace code [i] based on linear OOA(965, 2796201, F9, 3, 10) (dual of [(2796201, 3), 8388538, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(3130, 5592402, F3, 3, 10) (dual of [(5592402, 3), 16777076, 11]-NRT-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(3193, 7579182, F3, 15, 10) (dual of [(7579182, 15), 113687537, 11]-NRT-code) | [i] | OOA Stacking with Additional Row | |