Information on Result #1299146
Linear OA(3213, 247, F3, 105) (dual of [247, 34, 106]-code), using construction X with Varšamov bound based on
- linear OA(3195, 227, F3, 105) (dual of [227, 32, 106]-code), using
- 17 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
- 17 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3195, 229, F3, 92) (dual of [229, 34, 93]-code), using Gilbert–Varšamov bound and bm = 3195 > Vbs−1(k−1) = 799 433715 099322 594045 744764 891520 863474 354582 012081 484023 550396 046526 293310 935079 606192 942545 [i]
- linear OA(316, 18, F3, 12) (dual of [18, 2, 13]-code), using
- 2 times truncation [i] based on linear OA(318, 20, F3, 14) (dual of [20, 2, 15]-code), using
- repeating each code word 5 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 5 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(318, 20, F3, 14) (dual of [20, 2, 15]-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(3213, 247, F3, 104) (dual of [247, 34, 105]-code) | [i] | Strength Reduction | |