Information on Result #700440
Linear OA(25633, 65556, F256, 14) (dual of [65556, 65523, 15]-code), using construction X applied to Ce(13) ⊂ Ce(6) based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2566, 20, F256, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,256)), using
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), using
- Reed–Solomon code RS(250,256) [i]
- discarding factors / shortening the dual code based on linear OA(2566, 256, F256, 6) (dual of [256, 250, 7]-code or 256-arc in PG(5,256)), 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 | OA(12838, 65556, S128, 14) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25633, 54797, F256, 2, 14) (dual of [(54797, 2), 109561, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25633, 54797, F256, 3, 14) (dual of [(54797, 3), 164358, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(25633, 54797, F256, 4, 14) (dual of [(54797, 4), 219155, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(25633, 54797, F256, 5, 14) (dual of [(54797, 5), 273952, 15]-NRT-code) | [i] | ||
| 6 | Linear OOA(25633, 54797, F256, 6, 14) (dual of [(54797, 6), 328749, 15]-NRT-code) | [i] | ||
| 7 | Digital (19, 33, 54797)-net over F256 | [i] | ||
| 8 | Linear OOA(25633, 32778, F256, 2, 14) (dual of [(32778, 2), 65523, 15]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25633, 21852, F256, 3, 14) (dual of [(21852, 3), 65523, 15]-NRT-code) | [i] | ||
| 10 | Linear OOA(25633, 16389, F256, 4, 14) (dual of [(16389, 4), 65523, 15]-NRT-code) | [i] | ||
| 11 | Linear OOA(25633, 13111, F256, 5, 14) (dual of [(13111, 5), 65522, 15]-NRT-code) | [i] | ||
| 12 | Linear OOA(25633, 10926, F256, 6, 14) (dual of [(10926, 6), 65523, 15]-NRT-code) | [i] | ||
| 13 | Linear OOA(25633, 9365, F256, 14, 14) (dual of [(9365, 14), 131077, 15]-NRT-code) | [i] | OA Folding and Stacking | |