Information on Result #1299483
Linear OA(3243, 277, F3, 123) (dual of [277, 34, 124]-code), using construction X with Varšamov bound based on
- linear OA(3219, 251, F3, 124) (dual of [251, 32, 125]-code), using
- construction XX applied to Ce(124) ⊂ Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3217, 243, F3, 125) (dual of [243, 26, 126]-code), using an extension Ce(124) of the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,124], and designed minimum distance d ≥ |I|+1 = 125 [i]
- 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(31, 7, F3, 1) (dual of [7, 6, 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
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(124) ⊂ Ce(121) ⊂ Ce(120) [i] based on
- linear OA(3219, 253, F3, 105) (dual of [253, 34, 106]-code), using Gilbert–Varšamov bound and bm = 3219 > Vbs−1(k−1) = 240 894835 116651 154791 624421 777502 174756 332312 880253 790665 222907 137908 196510 145890 778379 018808 142897 216689 [i]
- 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
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(3243, 277, F3, 122) (dual of [277, 34, 123]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3242, 276, F3, 122) (dual of [276, 34, 123]-code) | [i] | Truncation | |
| 3 | Linear OA(3241, 275, F3, 121) (dual of [275, 34, 122]-code) | [i] | ||