Information on Result #1314428
Linear OA(2553, 892, F25, 23) (dual of [892, 839, 24]-code), using 256 step Varšamov–Edel lengthening with (ri) = (3, 0, 1, 4 times 0, 1, 15 times 0, 1, 40 times 0, 1, 78 times 0, 1, 112 times 0) based on linear OA(2545, 628, F25, 23) (dual of [628, 583, 24]-code), using
- construction XX applied to C1 = C([623,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([623,21]) [i] based on
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2543, 624, F25, 22) (dual of [624, 581, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2545, 624, F25, 23) (dual of [624, 579, 24]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2541, 624, F25, 21) (dual of [624, 583, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 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
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
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(2553, 892, F25, 2, 23) (dual of [(892, 2), 1731, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (30, 53, 892)-net over F25 | [i] | ||
| 3 | Linear OOA(2553, 446, F25, 2, 23) (dual of [(446, 2), 839, 24]-NRT-code) | [i] | OOA Folding | |