Information on Result #682216
Linear OA(5143, 1953161, F5, 19) (dual of [1953161, 1953018, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(15) ⊂ Ce(13) 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(5109, 1953125, F5, 16) (dual of [1953125, 1953016, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(5100, 1953125, F5, 14) (dual of [1953125, 1953025, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(54, 33, F5, 2) (dual of [33, 29, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(54, 124, F5, 2) (dual of [124, 120, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(54, 124, F5, 2) (dual of [124, 120, 3]-code), using
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- Reed–Solomon code RS(4,5) [i]
- discarding factors / shortening the dual code based on linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
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(5143, 1236905, F5, 2, 19) (dual of [(1236905, 2), 2473667, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5143, 1236905, F5, 3, 19) (dual of [(1236905, 3), 3710572, 20]-NRT-code) | [i] | ||
| 3 | Digital (124, 143, 1236905)-net over F5 | [i] | ||