Information on Result #683191
Linear OA(583, 3133, F5, 21) (dual of [3133, 3050, 22]-code), using construction XX applied to Ce(20) ⊂ Ce(18) ⊂ Ce(17) based on
- linear OA(581, 3125, F5, 21) (dual of [3125, 3044, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(51, 7, F5, 1) (dual of [7, 6, 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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(583, 2047, F5, 2, 21) (dual of [(2047, 2), 4011, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(583, 2047, F5, 3, 21) (dual of [(2047, 3), 6058, 22]-NRT-code) | [i] | ||
| 3 | Digital (62, 83, 2047)-net over F5 | [i] | ||
| 4 | Linear OOA(583, 1566, F5, 2, 21) (dual of [(1566, 2), 3049, 22]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(583, 1044, F5, 3, 21) (dual of [(1044, 3), 3049, 22]-NRT-code) | [i] | ||