Information on Result #1314361
Linear OA(2529, 1001, F25, 12) (dual of [1001, 972, 13]-code), using 367 step Varšamov–Edel lengthening with (ri) = (2, 1, 5 times 0, 1, 28 times 0, 1, 105 times 0, 1, 224 times 0) based on linear OA(2523, 628, F25, 12) (dual of [628, 605, 13]-code), using
- construction XX applied to C1 = C([623,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([623,10]) [i] based on
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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(2529, 1001, F25, 2, 12) (dual of [(1001, 2), 1973, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (17, 29, 1001)-net over F25 | [i] | ||
| 3 | Linear OOA(2529, 500, F25, 2, 12) (dual of [(500, 2), 971, 13]-NRT-code) | [i] | OOA Folding | |