Information on Result #682353
Linear OA(5126, 390655, F5, 19) (dual of [390655, 390529, 20]-code), using construction XX applied to Ce(18) ⊂ Ce(15) ⊂ Ce(13) based on
- linear OA(5121, 390625, F5, 19) (dual of [390625, 390504, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(589, 390625, F5, 14) (dual of [390625, 390536, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(53, 28, F5, 2) (dual of [28, 25, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- discarding factors / shortening the dual code based on linear OA(53, 31, F5, 2) (dual of [31, 28, 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(5126, 247372, F5, 2, 19) (dual of [(247372, 2), 494618, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5126, 247372, F5, 3, 19) (dual of [(247372, 3), 741990, 20]-NRT-code) | [i] | ||
| 3 | Digital (107, 126, 247372)-net over F5 | [i] | ||
| 4 | Linear OOA(5126, 130218, F5, 3, 19) (dual of [(130218, 3), 390528, 20]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(5126, 43406, F5, 19, 19) (dual of [(43406, 19), 824588, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |