Information on Result #893830
Linear OOA(3204, 4782992, F3, 2, 16) (dual of [(4782992, 2), 9565780, 17]-NRT-code), using trace code based on linear OOA(9102, 2391496, F9, 2, 16) (dual of [(2391496, 2), 4782890, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9102, 4782992, F9, 16) (dual of [4782992, 4782890, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(9102, 4782993, F9, 16) (dual of [4782993, 4782891, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(12) [i] based on
- linear OA(999, 4782969, F9, 16) (dual of [4782969, 4782870, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(15) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(9102, 4782993, F9, 16) (dual of [4782993, 4782891, 17]-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(3205, 4782992, F3, 2, 16) (dual of [(4782992, 2), 9565779, 17]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3204, 2391496, F3, 4, 16) (dual of [(2391496, 4), 9565780, 17]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3204, 1195747, F3, 18, 16) (dual of [(1195747, 18), 21523242, 17]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |