Information on Result #682851
Linear OA(557, 15634, F5, 12) (dual of [15634, 15577, 13]-code), using construction XX applied to Ce(11) ⊂ Ce(10) ⊂ Ce(8) based on
- linear OA(555, 15625, F5, 12) (dual of [15625, 15570, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(549, 15625, F5, 11) (dual of [15625, 15576, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(543, 15625, F5, 9) (dual of [15625, 15582, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(50, 7, F5, 0) (dual of [7, 7, 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
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(557, 9286, F5, 2, 12) (dual of [(9286, 2), 18515, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(557, 9286, F5, 3, 12) (dual of [(9286, 3), 27801, 13]-NRT-code) | [i] | ||
| 3 | Digital (45, 57, 9286)-net over F5 | [i] | ||
| 4 | Linear OOA(557, 7817, F5, 2, 12) (dual of [(7817, 2), 15577, 13]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(557, 5211, F5, 3, 12) (dual of [(5211, 3), 15576, 13]-NRT-code) | [i] | ||