Information on Result #1646116
Linear OOA(3173, 398938, F3, 5, 20) (dual of [(398938, 5), 1994517, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3173, 398938, F3, 3, 20) (dual of [(398938, 3), 1196641, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3173, 531446, F3, 3, 20) (dual of [(531446, 3), 1594165, 21]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3172, 531446, F3, 3, 20) (dual of [(531446, 3), 1594166, 21]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3172, 1594338, F3, 20) (dual of [1594338, 1594166, 21]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3170, 1594336, F3, 20) (dual of [1594336, 1594166, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(3157, 1594323, F3, 19) (dual of [1594323, 1594166, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(30, 13, F3, 0) (dual of [13, 13, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3170, 1594336, F3, 20) (dual of [1594336, 1594166, 21]-code), using
- OOA 3-folding [i] based on linear OA(3172, 1594338, F3, 20) (dual of [1594338, 1594166, 21]-code), using
- 31 times duplication [i] based on linear OOA(3172, 531446, F3, 3, 20) (dual of [(531446, 3), 1594166, 21]-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(3173, 199468, F3, 25, 20) (dual of [(199468, 25), 4986527, 21]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |