Information on Result #1013921
Linear OOA(788, 274537, F7, 3, 13) (dual of [(274537, 3), 823523, 14]-NRT-code), using (u, u+v)-construction based on
- linear OOA(710, 21, F7, 3, 6) (dual of [(21, 3), 53, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;21,7) [i]
- linear OOA(77, 13, F7, 3, 6) (dual of [(13, 3), 32, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- extracting embedded OOA [i] based on digital (1, 7, 13)-net over F7, using
- linear OOA(73, 8, F7, 3, 3) (dual of [(8, 3), 21, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(778, 274516, F7, 3, 13) (dual of [(274516, 3), 823470, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(778, 823548, F7, 13) (dual of [823548, 823470, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(778, 823550, F7, 13) (dual of [823550, 823472, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(778, 823543, F7, 13) (dual of [823543, 823465, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(70, 7, F7, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(778, 823550, F7, 13) (dual of [823550, 823472, 14]-code), using
- OOA 3-folding [i] based on linear OA(778, 823548, F7, 13) (dual of [823548, 823470, 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(788, 137268, F7, 15, 13) (dual of [(137268, 15), 2058932, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |