Information on Result #1310544
Linear OA(578, 3259, F5, 18) (dual of [3259, 3181, 19]-code), using 117 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 13 times 0, 1, 30 times 0, 1, 63 times 0) based on linear OA(572, 3136, F5, 18) (dual of [3136, 3064, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(15) [i] based on
- 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(561, 3125, F5, 16) (dual of [3125, 3064, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(51, 11, F5, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-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(578, 3259, F5, 2, 18) (dual of [(3259, 2), 6440, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(578, 3259, F5, 3, 18) (dual of [(3259, 3), 9699, 19]-NRT-code) | [i] | ||
| 3 | Digital (60, 78, 3259)-net over F5 | [i] | ||
| 4 | Linear OOA(578, 1629, F5, 2, 18) (dual of [(1629, 2), 3180, 19]-NRT-code) | [i] | OOA Folding | |