Information on Result #683004
Linear OA(572, 3136, F5, 18) (dual of [3136, 3064, 19]-code), using construction X applied to Ce(17) ⊂ Ce(15) 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: 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(573, 3137, F5, 18) (dual of [3137, 3064, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(572, 2138, F5, 2, 18) (dual of [(2138, 2), 4204, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(572, 2138, F5, 3, 18) (dual of [(2138, 3), 6342, 19]-NRT-code) | [i] | ||
| 4 | Digital (54, 72, 2138)-net over F5 | [i] | ||
| 5 | Linear OA(574, 3140, F5, 18) (dual of [3140, 3066, 19]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(575, 3147, F5, 18) (dual of [3147, 3072, 19]-code) | [i] | ||
| 7 | Linear OA(576, 3162, F5, 18) (dual of [3162, 3086, 19]-code) | [i] | ||
| 8 | Linear OA(577, 3194, F5, 18) (dual of [3194, 3117, 19]-code) | [i] | ||
| 9 | Linear OA(578, 3259, F5, 18) (dual of [3259, 3181, 19]-code) | [i] | ||
| 10 | Linear OA(579, 3383, F5, 18) (dual of [3383, 3304, 19]-code) | [i] | ||
| 11 | Linear OA(580, 3589, F5, 18) (dual of [3589, 3509, 19]-code) | [i] | ||
| 12 | Linear OOA(572, 1568, F5, 2, 18) (dual of [(1568, 2), 3064, 19]-NRT-code) | [i] | OOA Folding | |
| 13 | Linear OOA(572, 1045, F5, 3, 18) (dual of [(1045, 3), 3063, 19]-NRT-code) | [i] | ||
| 14 | Linear OOA(572, 348, F5, 18, 18) (dual of [(348, 18), 6192, 19]-NRT-code) | [i] | OA Folding and Stacking | |