Information on Result #1301895
Linear OA(5141, 78183, F5, 23) (dual of [78183, 78042, 24]-code), using construction X with Varšamov bound based on
- linear OA(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [i] based on
- linear OA(5127, 78125, F5, 23) (dual of [78125, 77998, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(512, 54, F5, 6) (dual of [54, 42, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- the cyclic code C(A) with length 62 | 53−1, defining set A = {4,8,11,17}, and minimum distance d ≥ |{8,11,14,…,23}|+1 = 7 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(512, 62, F5, 6) (dual of [62, 50, 7]-code), using
- construction X applied to Ce(22) ⊂ Ce(15) [i] based on
- linear OA(5139, 78181, F5, 22) (dual of [78181, 78042, 23]-code), using Gilbert–Varšamov bound and bm = 5139 > Vbs−1(k−1) = 488413 210814 076622 369628 964373 928239 773280 549482 200353 502881 535226 617139 321378 809333 547408 876785 [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
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(5141, 78183, F5, 2, 23) (dual of [(78183, 2), 156225, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5141, 78183, F5, 3, 23) (dual of [(78183, 3), 234408, 24]-NRT-code) | [i] | ||
| 3 | Digital (118, 141, 78183)-net over F5 | [i] | ||
| 4 | Linear OOA(5141, 39091, F5, 2, 23) (dual of [(39091, 2), 78041, 24]-NRT-code) | [i] | OOA Folding | |