Information on Result #1298924
Linear OA(3180, 215, F3, 84) (dual of [215, 35, 85]-code), using construction X with Varšamov bound based on
- linear OA(3177, 210, F3, 84) (dual of [210, 33, 85]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3174, 206, F3, 84) (dual of [206, 32, 85]-code), using
- 38 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
- 38 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- linear OA(3174, 207, F3, 81) (dual of [207, 33, 82]-code), using Gilbert–Varšamov bound and bm = 3174 > Vbs−1(k−1) = 57969 662298 850075 921507 641900 857889 503801 873617 000438 561035 717199 862035 457000 798841 [i]
- linear OA(32, 3, F3, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,3)), using
- dual of repetition code with length 3 [i]
- Reed–Solomon code RS(1,3) [i]
- linear OA(3174, 206, F3, 84) (dual of [206, 32, 85]-code), using
- construction X with Varšamov bound [i] based on
- 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(31, 3, F3, 1) (dual of [3, 2, 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
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
None.