Information on Result #1323776
Linear OA(5118, 1953179, F5, 15) (dual of [1953179, 1953061, 16]-code), using construction X applied to Ce(15) ⊂ Ce(8) based on
- 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(564, 1953125, F5, 9) (dual of [1953125, 1953061, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(59, 54, F5, 5) (dual of [54, 45, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(59, 62, F5, 5) (dual of [62, 53, 6]-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(5118, 1953179, F5, 2, 15) (dual of [(1953179, 2), 3906240, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5118, 1953179, F5, 3, 15) (dual of [(1953179, 3), 5859419, 16]-NRT-code) | [i] | ||
| 3 | Digital (103, 118, 1953179)-net over F5 | [i] | ||
| 4 | Linear OA(5119, 1953181, F5, 15) (dual of [1953181, 1953062, 16]-code) | [i] | Construction X with Varšamov Bound | |
| 5 | Linear OOA(5118, 976589, F5, 2, 15) (dual of [(976589, 2), 1953060, 16]-NRT-code) | [i] | OOA Folding | |