Information on Result #1550378
Linear OOA(5136, 44033, F5, 3, 24) (dual of [(44033, 3), 131963, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5136, 44033, F5, 24) (dual of [44033, 43897, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5136, 78142, F5, 24) (dual of [78142, 78006, 25]-code), using
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(51, 16, F5, 1) (dual of [16, 15, 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]
- construction XX applied to Ce(23) ⊂ Ce(21) ⊂ Ce(20) [i] based on
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(5136, 11008, F5, 27, 24) (dual of [(11008, 27), 297080, 25]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |