Information on Result #684311
Linear OA(570, 134, F5, 34) (dual of [134, 64, 35]-code), using construction XX applied to Ce(33) ⊂ Ce(31) ⊂ Ce(30) based on
- linear OA(568, 125, F5, 34) (dual of [125, 57, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(562, 125, F5, 32) (dual of [125, 63, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(561, 125, F5, 31) (dual of [125, 64, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(51, 8, F5, 1) (dual of [8, 7, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(570, 134, F5, 33) (dual of [134, 64, 34]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(572, 136, F5, 34) (dual of [136, 64, 35]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(573, 137, F5, 34) (dual of [137, 64, 35]-code) | [i] | ||
| 4 | Linear OA(569, 133, F5, 33) (dual of [133, 64, 34]-code) | [i] | Truncation | |
| 5 | Linear OA(568, 132, F5, 32) (dual of [132, 64, 33]-code) | [i] | ||
| 6 | Linear OOA(570, 67, F5, 2, 34) (dual of [(67, 2), 64, 35]-NRT-code) | [i] | OOA Folding | |