Information on Result #683226
Linear OA(543, 3133, F5, 11) (dual of [3133, 3090, 12]-code), using construction XX applied to Ce(10) ⊂ Ce(8) ⊂ Ce(7) based on
- linear OA(541, 3125, F5, 11) (dual of [3125, 3084, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(536, 3125, F5, 9) (dual of [3125, 3089, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(531, 3125, F5, 8) (dual of [3125, 3094, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(543, 1889, F5, 2, 11) (dual of [(1889, 2), 3735, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(543, 1889, F5, 3, 11) (dual of [(1889, 3), 5624, 12]-NRT-code) | [i] | ||
| 3 | Digital (32, 43, 1889)-net over F5 | [i] | ||
| 4 | Linear OOA(543, 1566, F5, 2, 11) (dual of [(1566, 2), 3089, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(543, 1044, F5, 3, 11) (dual of [(1044, 3), 3089, 12]-NRT-code) | [i] | ||