Information on Result #1523264
Linear OOA(3131, 23880, F3, 3, 19) (dual of [(23880, 3), 71509, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3131, 23880, F3, 2, 19) (dual of [(23880, 2), 47629, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3131, 29544, F3, 2, 19) (dual of [(29544, 2), 58957, 20]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3130, 29544, F3, 2, 19) (dual of [(29544, 2), 58958, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3130, 59088, F3, 19) (dual of [59088, 58958, 20]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3129, 59087, F3, 19) (dual of [59087, 58958, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3121, 59049, F3, 19) (dual of [59049, 58928, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(391, 59049, F3, 14) (dual of [59049, 58958, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(38, 38, F3, 4) (dual of [38, 30, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3129, 59087, F3, 19) (dual of [59087, 58958, 20]-code), using
- OOA 2-folding [i] based on linear OA(3130, 59088, F3, 19) (dual of [59088, 58958, 20]-code), using
- 31 times duplication [i] based on linear OOA(3130, 29544, F3, 2, 19) (dual of [(29544, 2), 58958, 20]-NRT-code), using
Mode: 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(3131, 11940, F3, 5, 19) (dual of [(11940, 5), 59569, 20]-NRT-code) | [i] | OOA Folding | |