Information on Result #684438
Linear OA(513, 32, F5, 7) (dual of [32, 19, 8]-code), using construction XX applied to Ce(6) ⊂ Ce(3) ⊂ Ce(2) based on
- linear OA(510, 25, F5, 7) (dual of [25, 15, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(55, 25, F5, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(587, 665, F5, 23) (dual of [665, 578, 24]-code) | [i] | Construction XX with Cyclic Codes | |
| 2 | Linear OA(593, 671, F5, 24) (dual of [671, 578, 25]-code) | [i] | ||
| 3 | Linear OA(5107, 668, F5, 29) (dual of [668, 561, 30]-code) | [i] | ||
| 4 | Linear OA(5113, 662, F5, 32) (dual of [662, 549, 33]-code) | [i] | ||
| 5 | Linear OA(5119, 679, F5, 32) (dual of [679, 560, 33]-code) | [i] | ||
| 6 | Linear OA(5119, 668, F5, 33) (dual of [668, 549, 34]-code) | [i] | ||
| 7 | Linear OA(5117, 665, F5, 33) (dual of [665, 548, 34]-code) | [i] | ||
| 8 | Linear OA(5124, 673, F5, 34) (dual of [673, 549, 35]-code) | [i] | ||
| 9 | Linear OA(5128, 673, F5, 35) (dual of [673, 545, 36]-code) | [i] | ||
| 10 | Linear OA(5133, 682, F5, 36) (dual of [682, 549, 37]-code) | [i] | ||
| 11 | Linear OA(5131, 679, F5, 36) (dual of [679, 548, 37]-code) | [i] | ||
| 12 | Linear OA(5128, 676, F5, 35) (dual of [676, 548, 36]-code) | [i] | ||
| 13 | Linear OA(5137, 683, F5, 37) (dual of [683, 546, 38]-code) | [i] | ||
| 14 | Linear OA(5136, 672, F5, 38) (dual of [672, 536, 39]-code) | [i] | ||
| 15 | Linear OA(5133, 665, F5, 38) (dual of [665, 532, 39]-code) | [i] | ||
| 16 | Linear OA(5140, 672, F5, 39) (dual of [672, 532, 40]-code) | [i] | ||
| 17 | Linear OA(5147, 679, F5, 40) (dual of [679, 532, 41]-code) | [i] | ||
| 18 | Linear OA(5144, 672, F5, 41) (dual of [672, 528, 42]-code) | [i] | ||
| 19 | Linear OA(5148, 672, F5, 42) (dual of [672, 524, 43]-code) | [i] | ||
| 20 | Linear OA(5149, 665, F5, 43) (dual of [665, 516, 44]-code) | [i] | ||