Information on Result #1550173
Linear OOA(5132, 78174, F5, 3, 22) (dual of [(78174, 3), 234390, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5132, 78174, F5, 22) (dual of [78174, 78042, 23]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- linear OA(5129, 78171, F5, 20) (dual of [78171, 78042, 21]-code), using Gilbert–Varšamov bound and bm = 5129 > Vbs−1(k−1) = 2093 551392 438519 134033 978849 958649 341280 527566 061387 058850 326452 192060 758815 302799 882169 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(5129, 78169, F5, 22) (dual of [78169, 78040, 23]-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(5132, 19543, F5, 27, 22) (dual of [(19543, 27), 527529, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |