Information on Result #699182
Linear OA(8113, 531444, F81, 5) (dual of [531444, 531431, 6]-code), using construction X applied to Ce(4) ⊂ Ce(3) based on
- linear OA(8113, 531441, F81, 5) (dual of [531441, 531428, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(8110, 531441, F81, 4) (dual of [531441, 531431, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-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(926, 1062888, F9, 5) (dual of [1062888, 1062862, 6]-code) | [i] | Trace Code | |
| 2 | Linear OOA(8113, 531444, F81, 2, 5) (dual of [(531444, 2), 1062875, 6]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(8113, 531444, F81, 3, 5) (dual of [(531444, 3), 1594319, 6]-NRT-code) | [i] | ||
| 4 | Linear OOA(8113, 531444, F81, 4, 5) (dual of [(531444, 4), 2125763, 6]-NRT-code) | [i] | ||
| 5 | Linear OOA(8113, 265722, F81, 2, 5) (dual of [(265722, 2), 531431, 6]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(8113, 265721, F81, 3, 5) (dual of [(265721, 3), 797150, 6]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 7 | Linear OOA(8113, 265721, F81, 4, 5) (dual of [(265721, 4), 1062871, 6]-NRT-code) | [i] | ||