Information on Result #700438
Linear OA(25637, 65556, F256, 16) (dual of [65556, 65519, 17]-code), using construction X applied to Ce(15) ⊂ Ce(8) based on
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(12843, 65556, S128, 16) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(25637, 36937, F256, 2, 16) (dual of [(36937, 2), 73837, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25637, 36937, F256, 3, 16) (dual of [(36937, 3), 110774, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(25637, 36937, F256, 4, 16) (dual of [(36937, 4), 147711, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(25637, 36937, F256, 5, 16) (dual of [(36937, 5), 184648, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(25637, 36937, F256, 6, 16) (dual of [(36937, 6), 221585, 17]-NRT-code) | [i] | ||
| 7 | Digital (21, 37, 36937)-net over F256 | [i] | ||
| 8 | Linear OOA(25637, 32778, F256, 2, 16) (dual of [(32778, 2), 65519, 17]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(25637, 21852, F256, 3, 16) (dual of [(21852, 3), 65519, 17]-NRT-code) | [i] | ||
| 10 | Linear OOA(25637, 16389, F256, 4, 16) (dual of [(16389, 4), 65519, 17]-NRT-code) | [i] | ||
| 11 | Linear OOA(25637, 13111, F256, 5, 16) (dual of [(13111, 5), 65518, 17]-NRT-code) | [i] | ||
| 12 | Linear OOA(25637, 10926, F256, 6, 16) (dual of [(10926, 6), 65519, 17]-NRT-code) | [i] | ||