Information on Result #1314332
Linear OA(2513, 657, F25, 6) (dual of [657, 644, 7]-code), using 25 step Varšamov–Edel lengthening with (ri) = (1, 24 times 0) based on linear OA(2512, 631, F25, 6) (dual of [631, 619, 7]-code), using
- construction XX applied to C1 = C([622,2]), C2 = C([0,3]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([622,3]) [i] based on
- linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(257, 624, F25, 4) (dual of [624, 617, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−2,−1,…,3}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(255, 624, F25, 3) (dual of [624, 619, 4]-code or 624-cap in PG(4,25)), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- Reed–Solomon code RS(24,25) [i]
- discarding factors / shortening the dual code based on linear OA(251, 25, F25, 1) (dual of [25, 24, 2]-code), using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: 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(2513, 657, F25, 2, 6) (dual of [(657, 2), 1301, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (7, 13, 657)-net over F25 | [i] | ||
| 3 | Linear OOA(2513, 328, F25, 2, 6) (dual of [(328, 2), 643, 7]-NRT-code) | [i] | OOA Folding | |