Information on Result #1725349
Linear OOA(791, 2882410, F7, 15, 13) (dual of [(2882410, 15), 43236059, 14]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(791, 5764821, F7, 3, 13) (dual of [(5764821, 3), 17294372, 14]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(791, 5764821, F7, 13) (dual of [5764821, 5764730, 14]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(790, 5764819, F7, 13) (dual of [5764819, 5764729, 14]-code), using
- construction X4 applied to Ce(12) ⊂ Ce(10) [i] based on
- linear OA(789, 5764801, F7, 13) (dual of [5764801, 5764712, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(773, 5764801, F7, 11) (dual of [5764801, 5764728, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(717, 18, F7, 17) (dual of [18, 1, 18]-code or 18-arc in PG(16,7)), using
- dual of repetition code with length 18 [i]
- linear OA(71, 18, F7, 1) (dual of [18, 17, 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(12) ⊂ Ce(10) [i] based on
- linear OA(790, 5764820, F7, 12) (dual of [5764820, 5764730, 13]-code), using Gilbert–Varšamov bound and bm = 790 > Vbs−1(k−1) = 2123 960660 218861 187732 971678 039600 392570 059293 777703 896304 444695 670364 218839 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 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
- linear OA(790, 5764819, F7, 13) (dual of [5764819, 5764729, 14]-code), using
- construction X with Varšamov bound [i] based on
Mode: Linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (78, 91, 2882410)-net over F7 | [i] | Net Defined by OOA | |