Information on Result #1013890
Linear OOA(780, 274533, F7, 3, 12) (dual of [(274533, 3), 823519, 13]-NRT-code), using (u, u+v)-construction based on
- 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(773, 274520, F7, 3, 12) (dual of [(274520, 3), 823487, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(773, 823560, F7, 12) (dual of [823560, 823487, 13]-code), using
- 1 times code embedding in larger space [i] based on linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code), using
- construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
- 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(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(715, 16, F7, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,7)), using
- dual of repetition code with length 16 [i]
- linear OA(71, 16, F7, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(71, 342, F7, 1) (dual of [342, 341, 2]-code), using
- construction X4 applied to Ce(11) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code), using
- OOA 3-folding [i] based on linear OA(773, 823560, F7, 12) (dual of [823560, 823487, 13]-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(780, 137266, F7, 15, 12) (dual of [(137266, 15), 2058910, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |