Information on Result #1549170
Linear OOA(5110, 78173, F5, 3, 18) (dual of [(78173, 3), 234409, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5110, 78173, F5, 18) (dual of [78173, 78063, 19]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5108, 78169, F5, 18) (dual of [78169, 78061, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(17) ⊂ Ce(11) [i] based on
- linear OA(5108, 78171, F5, 17) (dual of [78171, 78063, 18]-code), using Gilbert–Varšamov bound and bm = 5108 > Vbs−1(k−1) = 398 416714 916402 843784 789032 765420 810286 018765 457070 530384 595462 281831 413689 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5108, 78169, F5, 18) (dual of [78169, 78061, 19]-code), using
Mode: 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(5110, 26057, F5, 21, 18) (dual of [(26057, 21), 547087, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |