Information on Result #1299226
Linear OA(3203, 241, F3, 95) (dual of [241, 38, 96]-code), using construction X with Varšamov bound based on
- linear OA(3200, 236, F3, 95) (dual of [236, 36, 96]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3185, 217, F3, 95) (dual of [217, 32, 96]-code), using
- 27 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
- 27 times truncation [i] based on linear OA(3212, 244, F3, 122) (dual of [244, 32, 123]-code), using
- 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(311, 15, F3, 8) (dual of [15, 4, 9]-code), using
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
- linear OA(310, 13, F3, 8) (dual of [13, 3, 9]-code), using the expurgated narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [0,6], and minimum distance d ≥ |{−1,0,…,6}|+1 = 9 (BCH-bound) [i]
- linear OA(39, 13, F3, 6) (dual of [13, 4, 7]-code), using the narrow-sense BCH-code C(I) with length 13 | 33−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(31, 2, F3, 1) (dual of [2, 1, 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
- construction X applied to C([0,6]) ⊂ C([1,6]) [i] based on
- linear OA(3185, 217, F3, 95) (dual of [217, 32, 96]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3200, 238, F3, 93) (dual of [238, 38, 94]-code), using Gilbert–Varšamov bound and bm = 3200 > Vbs−1(k−1) = 214425 906480 957112 889360 248320 235157 841749 831967 286077 194367 365636 820736 446306 822930 883256 855635 [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 (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(3204, 243, F3, 95) (dual of [243, 39, 96]-code) | [i] | Construction X with Varšamov Bound | |