Information on Result #737506
Linear OA(5120, 78160, F5, 21) (dual of [78160, 78040, 22]-code), using construction X applied to Ce(20) ⊂ Ce(15) based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(57, 35, F5, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 44, F5, 4) (dual of [44, 37, 5]-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 OA(5119, 78159, F5, 20) (dual of [78159, 78040, 21]-code) | [i] | Truncation | |
| 2 | Linear OA(5123, 78165, F5, 21) (dual of [78165, 78042, 22]-code) | [i] | Construction X with Varšamov Bound | |
| 3 | Linear OOA(5120, 39080, F5, 2, 21) (dual of [(39080, 2), 78040, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(5120, 26053, F5, 3, 21) (dual of [(26053, 3), 78039, 22]-NRT-code) | [i] | ||