Information on Result #1299284
Linear OA(3227, 261, F3, 114) (dual of [261, 34, 115]-code), using construction X with Varšamov bound based on
- linear OA(3204, 236, F3, 114) (dual of [236, 32, 115]-code), using
- 8 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- construction X applied to Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3212, 243, F3, 122) (dual of [243, 31, 123]-code), using an extension Ce(121) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,121], and designed minimum distance d ≥ |I|+1 = 122 [i]
- linear OA(3211, 243, F3, 121) (dual of [243, 32, 122]-code), using an extension Ce(120) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,120], and designed minimum distance d ≥ |I|+1 = 121 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 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(121) ⊂ Ce(120) [i] based on
- 8 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3204, 238, F3, 97) (dual of [238, 34, 98]-code), using Gilbert–Varšamov bound and bm = 3204 > Vbs−1(k−1) = 18 863664 458159 506073 809372 113773 189260 692797 905328 139299 006095 653189 854900 387194 473157 161964 874835 [i]
- linear OA(321, 23, F3, 16) (dual of [23, 2, 17]-code), using
- 1 times truncation [i] based on linear OA(322, 24, F3, 17) (dual of [24, 2, 18]-code), using
- repeating each code word 6 times [i] based on linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- extended Reed–Solomon code RSe(2,3) [i]
- Hamming code H(2,3) [i]
- Simplex code S(2,3) [i]
- the Tetracode [i]
- repeating each code word 6 times [i] based on linear OA(32, 4, F3, 2) (dual of [4, 2, 3]-code or 4-arc in PG(1,3)), using
- 1 times truncation [i] based on linear OA(322, 24, F3, 17) (dual of [24, 2, 18]-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 OA(3227, 261, F3, 113) (dual of [261, 34, 114]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3225, 259, F3, 112) (dual of [259, 34, 113]-code) | [i] | Truncation | |