Information on Result #1310414
Linear OA(545, 663, F5, 13) (dual of [663, 618, 14]-code), using 27 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 16 times 0) based on linear OA(541, 632, F5, 13) (dual of [632, 591, 14]-code), using
- construction XX applied to C1 = C([623,10]), C2 = C([0,11]), C3 = C1 + C2 = C([0,10]), and C∩ = C1 ∩ C2 = C([623,11]) [i] based on
- linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(541, 624, F5, 13) (dual of [624, 583, 14]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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(545, 663, F5, 2, 13) (dual of [(663, 2), 1281, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(545, 663, F5, 3, 13) (dual of [(663, 3), 1944, 14]-NRT-code) | [i] | ||
| 3 | Digital (32, 45, 663)-net over F5 | [i] | ||
| 4 | Linear OOA(545, 331, F5, 2, 13) (dual of [(331, 2), 617, 14]-NRT-code) | [i] | OOA Folding | |