Information on Result #1299006
Linear OA(3186, 222, F3, 87) (dual of [222, 36, 88]-code), using construction X with Varšamov bound based on
- linear OA(3185, 220, F3, 87) (dual of [220, 35, 88]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3177, 209, F3, 87) (dual of [209, 32, 88]-code), using
- 35 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
- 35 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3177, 212, F3, 82) (dual of [212, 35, 83]-code), using Gilbert–Varšamov bound and bm = 3177 > Vbs−1(k−1) = 2 076551 592417 161795 237968 439977 987255 823366 133971 125777 993064 114320 394722 656246 022363 [i]
- linear OA(35, 8, F3, 4) (dual of [8, 3, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(35, 11, F3, 4) (dual of [11, 6, 5]-code), using
- Golay code G(3) [i]
- discarding factors / shortening the dual code based on linear OA(35, 11, F3, 4) (dual of [11, 6, 5]-code), using
- linear OA(3177, 209, F3, 87) (dual of [209, 32, 88]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3185, 221, F3, 86) (dual of [221, 36, 87]-code), using Gilbert–Varšamov bound and bm = 3185 > Vbs−1(k−1) = 16891 412246 536259 040630 456441 103759 611724 683014 169766 553778 874066 951905 156009 630490 494513 [i]
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code) (see above)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(3187, 224, F3, 87) (dual of [224, 37, 88]-code) | [i] | Construction X with Varšamov Bound | |