Information on Result #682455
Linear OA(5116, 78142, F5, 21) (dual of [78142, 78026, 22]-code), using construction X applied to Ce(20) ⊂ Ce(17) 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(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(53, 17, F5, 2) (dual of [17, 14, 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
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(5116, 39071, F5, 2, 21) (dual of [(39071, 2), 78026, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5116, 26047, F5, 3, 21) (dual of [(26047, 3), 78025, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(5116, 7814, F5, 21, 21) (dual of [(7814, 21), 163978, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |