Information on Result #1607011
Linear OOA(3179, 174680, F3, 4, 22) (dual of [(174680, 4), 698541, 23]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3179, 174680, F3, 3, 22) (dual of [(174680, 3), 523861, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3179, 177162, F3, 3, 22) (dual of [(177162, 3), 531307, 23]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3178, 177162, F3, 3, 22) (dual of [(177162, 3), 531308, 23]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3178, 531486, F3, 22) (dual of [531486, 531308, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(3169, 531441, F3, 22) (dual of [531441, 531272, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3133, 531441, F3, 17) (dual of [531441, 531308, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- OOA 3-folding [i] based on linear OA(3178, 531486, F3, 22) (dual of [531486, 531308, 23]-code), using
- 31 times duplication [i] based on linear OOA(3178, 177162, F3, 3, 22) (dual of [(177162, 3), 531308, 23]-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(3179, 58226, F3, 28, 22) (dual of [(58226, 28), 1630149, 23]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |