Information on Result #682561
Linear OA(566, 78135, F5, 12) (dual of [78135, 78069, 13]-code), using construction XX applied to Ce(11) ⊂ Ce(10) ⊂ Ce(8) based on
- linear OA(564, 78125, F5, 12) (dual of [78125, 78061, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(557, 78125, F5, 11) (dual of [78125, 78068, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(50, 8, F5, 0) (dual of [8, 8, 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(566, 39550, F5, 2, 12) (dual of [(39550, 2), 79034, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(566, 39550, F5, 3, 12) (dual of [(39550, 3), 118584, 13]-NRT-code) | [i] | ||
| 3 | Digital (54, 66, 39550)-net over F5 | [i] | ||
| 4 | Linear OOA(566, 26045, F5, 3, 12) (dual of [(26045, 3), 78069, 13]-NRT-code) | [i] | OOA Folding | |