Information on Result #1310574
Linear OA(583, 3356, F5, 19) (dual of [3356, 3273, 20]-code), using 219 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 4 times 0, 1, 12 times 0, 1, 27 times 0, 1, 57 times 0, 1, 112 times 0) based on linear OA(576, 3130, F5, 19) (dual of [3130, 3054, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(576, 3125, F5, 19) (dual of [3125, 3049, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(571, 3125, F5, 18) (dual of [3125, 3054, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(50, 5, F5, 0) (dual of [5, 5, 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(583, 3356, F5, 2, 19) (dual of [(3356, 2), 6629, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(583, 3356, F5, 3, 19) (dual of [(3356, 3), 9985, 20]-NRT-code) | [i] | ||
| 3 | Digital (64, 83, 3356)-net over F5 | [i] | ||
| 4 | Linear OOA(583, 1678, F5, 2, 19) (dual of [(1678, 2), 3273, 20]-NRT-code) | [i] | OOA Folding | |