Information on Result #1644818
Linear OOA(3153, 204046, F3, 5, 18) (dual of [(204046, 5), 1020077, 19]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3153, 204046, F3, 2, 18) (dual of [(204046, 2), 407939, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3153, 265742, F3, 2, 18) (dual of [(265742, 2), 531331, 19]-NRT-code), using
- 1 step truncation [i] based on linear OOA(3154, 265743, F3, 2, 19) (dual of [(265743, 2), 531332, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3154, 531486, F3, 19) (dual of [531486, 531332, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- linear OA(3145, 531441, F3, 19) (dual of [531441, 531296, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(39, 45, F3, 4) (dual of [45, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to Ce(18) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(3154, 531486, F3, 19) (dual of [531486, 531332, 20]-code), using
- 1 step truncation [i] based on linear OOA(3154, 265743, F3, 2, 19) (dual of [(265743, 2), 531332, 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(3153, 102022, F3, 25, 18) (dual of [(102022, 25), 2550397, 19]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |