Information on Result #1725524
Digital (51, 66, 5289)-net over F7, using net defined by OOA based on linear OOA(766, 5289, F7, 21, 15) (dual of [(5289, 21), 111003, 16]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(766, 15868, F7, 3, 15) (dual of [(15868, 3), 47538, 16]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(766, 15868, F7, 15) (dual of [15868, 15802, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(766, 16828, F7, 15) (dual of [16828, 16762, 16]-code), using
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [i] based on
- linear OA(761, 16807, F7, 15) (dual of [16807, 16746, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(74, 20, F7, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,7)), using
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(14) ⊂ Ce(10) ⊂ Ce(9) [i] based on
- discarding factors / shortening the dual code based on linear OA(766, 16828, F7, 15) (dual of [16828, 16762, 16]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(766, 15868, F7, 15) (dual of [15868, 15802, 16]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.