Information on Result #1550488
Linear OOA(5138, 976573, F5, 3, 19) (dual of [(976573, 3), 2929581, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(5138, 976573, F5, 2, 19) (dual of [(976573, 2), 1953008, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5138, 1953146, F5, 19) (dual of [1953146, 1953008, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(5137, 1953145, F5, 19) (dual of [1953145, 1953008, 20]-code), using
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- linear OA(5136, 1953125, F5, 19) (dual of [1953125, 1952989, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(5118, 1953125, F5, 17) (dual of [1953125, 1953007, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(519, 20, F5, 19) (dual of [20, 1, 20]-code or 20-arc in PG(18,5)), using
- dual of repetition code with length 20 [i]
- linear OA(51, 20, F5, 1) (dual of [20, 19, 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
- construction X4 applied to Ce(18) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(5137, 1953145, F5, 19) (dual of [1953145, 1953008, 20]-code), using
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(5138, 325524, F5, 21, 19) (dual of [(325524, 21), 6835866, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |