Information on Result #1324334
Linear OA(5148, 78189, F5, 24) (dual of [78189, 78041, 25]-code), using construction X with Varšamov bound based on
- linear OA(5147, 78187, F5, 24) (dual of [78187, 78040, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [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(513, 62, F5, 7) (dual of [62, 49, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(513, 63, F5, 7) (dual of [63, 50, 8]-code), using
- construction X applied to Ce(23) ⊂ Ce(15) [i] based on
- linear OA(5147, 78188, F5, 23) (dual of [78188, 78041, 24]-code), using Gilbert–Varšamov bound and bm = 5147 > Vbs−1(k−1) = 6954 415740 943782 753630 051600 992062 632249 132417 623138 635593 651920 378621 944793 628392 308548 326966 386525 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 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
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(5148, 78189, F5, 2, 24) (dual of [(78189, 2), 156230, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5148, 78189, F5, 3, 24) (dual of [(78189, 3), 234419, 25]-NRT-code) | [i] | ||
| 3 | Digital (124, 148, 78189)-net over F5 | [i] | ||
| 4 | Linear OOA(5148, 39094, F5, 2, 24) (dual of [(39094, 2), 78040, 25]-NRT-code) | [i] | OOA Folding | |