Information on Result #1310436
Linear OA(549, 678, F5, 14) (dual of [678, 629, 15]-code), using 42 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 10 times 0, 1, 26 times 0) based on linear OA(545, 632, F5, 14) (dual of [632, 587, 15]-code), using
- construction XX applied to C1 = C([623,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([623,12]) [i] based on
- 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(541, 624, F5, 13) (dual of [624, 583, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(545, 624, F5, 14) (dual of [624, 579, 15]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [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(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(549, 678, F5, 2, 14) (dual of [(678, 2), 1307, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(549, 678, F5, 3, 14) (dual of [(678, 3), 1985, 15]-NRT-code) | [i] | ||
| 3 | Digital (35, 49, 678)-net over F5 | [i] | ||
| 4 | Linear OOA(549, 339, F5, 2, 14) (dual of [(339, 2), 629, 15]-NRT-code) | [i] | OOA Folding | |