Information on Result #682519
Linear OA(5139, 78179, F5, 23) (dual of [78179, 78040, 24]-code), using construction X applied to Ce(22) ⊂ Ce(15) 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
Mode: Constructive and 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 OA(5140, 78180, F5, 23) (dual of [78180, 78040, 24]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(5141, 78181, F5, 23) (dual of [78181, 78040, 24]-code) | [i] | ||
| 3 | Linear OOA(5139, 78179, F5, 2, 23) (dual of [(78179, 2), 156219, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(5139, 78179, F5, 3, 23) (dual of [(78179, 3), 234398, 24]-NRT-code) | [i] | ||
| 5 | Digital (116, 139, 78179)-net over F5 | [i] | ||
| 6 | Linear OA(5140, 78181, F5, 23) (dual of [78181, 78041, 24]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(5141, 78183, F5, 23) (dual of [78183, 78042, 24]-code) | [i] | ||
| 8 | Linear OA(5142, 78185, F5, 23) (dual of [78185, 78043, 24]-code) | [i] | ||
| 9 | Linear OOA(5139, 39089, F5, 2, 23) (dual of [(39089, 2), 78039, 24]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(5139, 26059, F5, 3, 23) (dual of [(26059, 3), 78038, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(5139, 7107, F5, 23, 23) (dual of [(7107, 23), 163322, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |