Information on Result #711203
Linear OA(557, 632, F5, 18) (dual of [632, 575, 19]-code), using construction XX applied to C1 = C([623,15]), C2 = C([0,16]), C3 = C1 + C2 = C([0,15]), and C∩ = C1 ∩ C2 = C([623,16]) based on
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,15}, and designed minimum distance d ≥ |I|+1 = 18 [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(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(549, 624, F5, 16) (dual of [624, 575, 17]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,15], and designed minimum distance d ≥ |I|+1 = 17 [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: Constructive and 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 OA(560, 643, F5, 18) (dual of [643, 583, 19]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(561, 656, F5, 18) (dual of [656, 595, 19]-code) | [i] | ||
| 3 | Linear OA(562, 682, F5, 18) (dual of [682, 620, 19]-code) | [i] | ||
| 4 | Linear OA(563, 724, F5, 18) (dual of [724, 661, 19]-code) | [i] | ||
| 5 | Linear OA(564, 783, F5, 18) (dual of [783, 719, 19]-code) | [i] | ||
| 6 | Linear OA(565, 855, F5, 18) (dual of [855, 790, 19]-code) | [i] | ||
| 7 | Linear OA(566, 937, F5, 18) (dual of [937, 871, 19]-code) | [i] | ||
| 8 | Linear OA(567, 1029, F5, 18) (dual of [1029, 962, 19]-code) | [i] | ||
| 9 | Linear OOA(557, 316, F5, 2, 18) (dual of [(316, 2), 575, 19]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(557, 210, F5, 3, 18) (dual of [(210, 3), 573, 19]-NRT-code) | [i] | ||