Information on Result #1310507
Linear OA(559, 689, F5, 17) (dual of [689, 630, 18]-code), using 51 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 5 times 0, 1, 13 times 0, 1, 27 times 0) based on linear OA(554, 633, F5, 17) (dual of [633, 579, 18]-code), using
- construction XX applied to C1 = C([141,156]), C2 = C([143,157]), C3 = C1 + C2 = C([143,156]), and C∩ = C1 ∩ C2 = C([141,157]) [i] based on
- linear OA(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,156}, and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(549, 624, F5, 15) (dual of [624, 575, 16]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {143,144,…,157}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {141,142,…,157}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {143,144,…,156}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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(559, 689, F5, 2, 17) (dual of [(689, 2), 1319, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(559, 689, F5, 3, 17) (dual of [(689, 3), 2008, 18]-NRT-code) | [i] | ||
| 3 | Digital (42, 59, 689)-net over F5 | [i] | ||