Information on Result #893841
Linear OOA(3218, 4782992, F3, 2, 17) (dual of [(4782992, 2), 9565766, 18]-NRT-code), using trace code based on linear OOA(9109, 2391496, F9, 2, 17) (dual of [(2391496, 2), 4782883, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9109, 4782992, F9, 17) (dual of [4782992, 4782883, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(9109, 4782993, F9, 17) (dual of [4782993, 4782884, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(985, 4782969, F9, 14) (dual of [4782969, 4782884, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(93, 24, F9, 2) (dual of [24, 21, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(16) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(9109, 4782993, F9, 17) (dual of [4782993, 4782884, 18]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(3219, 4782992, F3, 2, 17) (dual of [(4782992, 2), 9565765, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3218, 2391496, F3, 4, 17) (dual of [(2391496, 4), 9565766, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3218, 1195747, F3, 18, 17) (dual of [(1195747, 18), 21523228, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |