Information on Result #905865
Linear OOA(25663, 33286, F256, 2, 23) (dual of [(33286, 2), 66509, 24]-NRT-code), using (u, u+v)-construction based on
- linear OOA(25617, 515, F256, 2, 11) (dual of [(515, 2), 1013, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2565, 257, F256, 2, 5) (dual of [(257, 2), 509, 6]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(2;509,256) [i]
- linear OOA(25612, 258, F256, 2, 11) (dual of [(258, 2), 504, 12]-NRT-code), using
- extracting embedded OOA [i] based on digital (1, 12, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- extracting embedded OOA [i] based on digital (1, 12, 258)-net over F256, using
- linear OOA(2565, 257, F256, 2, 5) (dual of [(257, 2), 509, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(25646, 32771, F256, 2, 23) (dual of [(32771, 2), 65496, 24]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- linear OA(25645, 65537, F256, 23) (dual of [65537, 65492, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to C([0,11]) ⊂ C([0,10]) [i] based on
- OOA 2-folding [i] based on linear OA(25646, 65542, F256, 23) (dual of [65542, 65496, 24]-code), 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 OOA(25663, 16643, F256, 4, 23) (dual of [(16643, 4), 66509, 24]-NRT-code) | [i] | OOA Folding | |