Information on Result #893840
Linear OOA(3216, 4782986, F3, 2, 17) (dual of [(4782986, 2), 9565756, 18]-NRT-code), using trace code based on linear OOA(9108, 2391493, F9, 2, 17) (dual of [(2391493, 2), 4782878, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(9108, 4782986, F9, 17) (dual of [4782986, 4782878, 18]-code), using
- construction XX applied to Ce(16) ⊂ Ce(14) ⊂ 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(992, 4782969, F9, 15) (dual of [4782969, 4782877, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(91, 16, F9, 1) (dual of [16, 15, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(16) ⊂ Ce(14) ⊂ Ce(13) [i] based on
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(3217, 4782986, F3, 2, 17) (dual of [(4782986, 2), 9565755, 18]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(3216, 2391493, F3, 4, 17) (dual of [(2391493, 4), 9565756, 18]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(3216, 1195746, F3, 18, 17) (dual of [(1195746, 18), 21523212, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |