Information on Result #1310567
Linear OA(566, 713, F5, 19) (dual of [713, 647, 20]-code), using 76 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 10 times 0, 1, 22 times 0, 1, 38 times 0) based on linear OA(561, 632, F5, 19) (dual of [632, 571, 20]-code), using
- construction XX applied to C1 = C([623,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([623,17]) [i] based on
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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(566, 713, F5, 2, 19) (dual of [(713, 2), 1360, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(566, 713, F5, 3, 19) (dual of [(713, 3), 2073, 20]-NRT-code) | [i] | ||
| 3 | Digital (47, 66, 713)-net over F5 | [i] | ||
| 4 | Linear OOA(566, 356, F5, 2, 19) (dual of [(356, 2), 646, 20]-NRT-code) | [i] | OOA Folding | |