Information on Result #682824
Linear OA(596, 15649, F5, 19) (dual of [15649, 15553, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(15) ⊂ Ce(13) based on
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(567, 15625, F5, 14) (dual of [15625, 15558, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(53, 22, F5, 2) (dual of [22, 19, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- linear OA(51, 2, F5, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [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(596, 14439, F5, 2, 19) (dual of [(14439, 2), 28782, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(596, 14439, F5, 3, 19) (dual of [(14439, 3), 43221, 20]-NRT-code) | [i] | ||
| 3 | Digital (77, 96, 14439)-net over F5 | [i] | ||
| 4 | Linear OOA(596, 5216, F5, 3, 19) (dual of [(5216, 3), 15552, 20]-NRT-code) | [i] | OOA Folding | |