Information on Result #674408
Linear OA(3158, 1594351, F3, 18) (dual of [1594351, 1594193, 19]-code), using construction X4 applied to Ce(18) ⊂ Ce(15) based on
- 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(3131, 1594323, F3, 16) (dual of [1594323, 1594192, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(327, 28, F3, 27) (dual of [28, 1, 28]-code or 28-arc in PG(26,3)), using
- dual of repetition code with length 28 [i]
- linear OA(31, 28, F3, 1) (dual of [28, 27, 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
Mode: Constructive and 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 OA(3159, 1594352, F3, 18) (dual of [1594352, 1594193, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(3160, 1594353, F3, 18) (dual of [1594353, 1594193, 19]-code) | [i] | ||
| 3 | Linear OA(3162, 1594356, F3, 18) (dual of [1594356, 1594194, 19]-code) | [i] | Construction X with Varšamov Bound | |