Information on Result #1299257
Linear OA(3224, 258, F3, 112) (dual of [258, 34, 113]-code), using construction X with Varšamov bound based on
- linear OA(3202, 234, F3, 112) (dual of [234, 32, 113]-code), using
- 10 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
- 10 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3202, 236, F3, 96) (dual of [236, 34, 97]-code), using Gilbert–Varšamov bound and bm = 3202 > Vbs−1(k−1) = 2 278638 945808 087567 485892 085145 468379 065686 417460 023423 009772 850310 815008 291503 689523 347072 346235 [i]
- linear OA(320, 22, F3, 15) (dual of [22, 2, 16]-code), using
- 2 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
- 2 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(3224, 258, F3, 111) (dual of [258, 34, 112]-code) | [i] | Strength Reduction | |