Information on Result #1648222
Linear OOA(3201, 1294104, F3, 5, 21) (dual of [(1294104, 5), 6470319, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3201, 1294104, F3, 3, 21) (dual of [(1294104, 3), 3882111, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3201, 1594334, F3, 3, 21) (dual of [(1594334, 3), 4782801, 22]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3200, 1594334, F3, 3, 21) (dual of [(1594334, 3), 4782802, 22]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3200, 4783002, F3, 21) (dual of [4783002, 4782802, 22]-code), using
- 2 times code embedding in larger space [i] based on linear OA(3198, 4783000, F3, 21) (dual of [4783000, 4782802, 22]-code), using
- construction X4 applied to C([0,10]) ⊂ C([0,9]) [i] based on
- linear OA(3197, 4782970, F3, 21) (dual of [4782970, 4782773, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(3169, 4782970, F3, 19) (dual of [4782970, 4782801, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(329, 30, F3, 29) (dual of [30, 1, 30]-code or 30-arc in PG(28,3)), using
- dual of repetition code with length 30 [i]
- linear OA(31, 30, F3, 1) (dual of [30, 29, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X4 applied to C([0,10]) ⊂ C([0,9]) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(3198, 4783000, F3, 21) (dual of [4783000, 4782802, 22]-code), using
- OOA 3-folding [i] based on linear OA(3200, 4783002, F3, 21) (dual of [4783002, 4782802, 22]-code), using
- 31 times duplication [i] based on linear OOA(3200, 1594334, F3, 3, 21) (dual of [(1594334, 3), 4782802, 22]-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(3201, 647051, F3, 25, 21) (dual of [(647051, 25), 16176074, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |