Information on Result #683142
Linear OA(5138, 3138, F5, 34) (dual of [3138, 3000, 35]-code), using construction XX applied to Ce(33) ⊂ Ce(31) ⊂ Ce(30) based on
- linear OA(5136, 3125, F5, 34) (dual of [3125, 2989, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(5126, 3125, F5, 32) (dual of [3125, 2999, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(5121, 3125, F5, 31) (dual of [3125, 3004, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 3124 = 55−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(51, 12, F5, 1) (dual of [12, 11, 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 OOA(5138, 3120, F5, 2, 34) (dual of [(3120, 2), 6102, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5138, 3120, F5, 3, 34) (dual of [(3120, 3), 9222, 35]-NRT-code) | [i] | ||
| 3 | Digital (104, 138, 3120)-net over F5 | [i] | ||
| 4 | Linear OOA(5138, 1569, F5, 2, 34) (dual of [(1569, 2), 3000, 35]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5138, 1046, F5, 3, 34) (dual of [(1046, 3), 3000, 35]-NRT-code) | [i] | ||