Information on Result #2306408
Linear OA(3191, 177207, F3, 24) (dual of [177207, 177016, 25]-code), using 1 times code embedding in larger space based on linear OA(3190, 177206, F3, 24) (dual of [177206, 177016, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3186, 177201, F3, 24) (dual of [177201, 177015, 25]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3177, 177148, F3, 25) (dual of [177148, 176971, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3133, 177148, F3, 19) (dual of [177148, 177015, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 177148 | 322−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(39, 53, F3, 4) (dual of [53, 44, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 34−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(39, 80, F3, 4) (dual of [80, 71, 5]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(3186, 177202, F3, 20) (dual of [177202, 177016, 21]-code), using Gilbert–Varšamov bound and bm = 3186 > Vbs−1(k−1) = 22643 141007 298843 796252 952422 023067 657245 483511 436960 962851 606964 294565 942149 319871 385923 [i]
- linear OA(33, 4, F3, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,3) or 4-cap in PG(2,3)), using
- dual of repetition code with length 4 [i]
- oval in PG(2, 3) [i]
- linear OA(3186, 177201, F3, 24) (dual of [177201, 177015, 25]-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 OOA(3191, 59069, F3, 3, 24) (dual of [(59069, 3), 177016, 25]-NRT-code) | [i] | OOA Folding | |