Information on Result #1301897
Linear OA(5142, 78185, F5, 23) (dual of [78185, 78043, 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, 78182, F5, 22) (dual of [78182, 78043, 23]-code), using Gilbert–Varšamov bound and bm = 5139 > Vbs−1(k−1) = 488544 437075 719871 198631 007757 800155 490924 422537 884517 481217 081023 098643 576526 826556 629305 555125 [i]
- linear OA(50, 3, F5, 0) (dual of [3, 3, 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(5142, 78185, F5, 2, 23) (dual of [(78185, 2), 156228, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5142, 78185, F5, 3, 23) (dual of [(78185, 3), 234413, 24]-NRT-code) | [i] | ||
| 3 | Digital (119, 142, 78185)-net over F5 | [i] | ||
| 4 | Linear OOA(5142, 39092, F5, 2, 23) (dual of [(39092, 2), 78042, 24]-NRT-code) | [i] | OOA Folding | |