Information on Result #677223
Linear OA(3218, 250, F3, 123) (dual of [250, 32, 124]-code), using construction X applied to Ce(124) ⊂ Ce(120) 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(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
Mode: Constructive and 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(3218, 250, F3, 122) (dual of [250, 32, 123]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(3218, 250, F3, 121) (dual of [250, 32, 122]-code) | [i] | ||
| 3 | Linear OA(3218, 250, F3, 120) (dual of [250, 32, 121]-code) | [i] | ||
| 4 | Linear OA(3218, 250, F3, 119) (dual of [250, 32, 120]-code) | [i] | ||
| 5 | Linear OA(3218, 250, F3, 118) (dual of [250, 32, 119]-code) | [i] | ||
| 6 | Linear OA(3218, 250, F3, 117) (dual of [250, 32, 118]-code) | [i] | ||
| 7 | Linear OA(3218, 250, F3, 116) (dual of [250, 32, 117]-code) | [i] | ||
| 8 | Linear OA(3218, 250, F3, 115) (dual of [250, 32, 116]-code) | [i] | ||
| 9 | Linear OA(3218, 250, F3, 114) (dual of [250, 32, 115]-code) | [i] | ||
| 10 | Linear OA(3218, 250, F3, 113) (dual of [250, 32, 114]-code) | [i] | ||
| 11 | Linear OA(3218, 250, F3, 112) (dual of [250, 32, 113]-code) | [i] | ||
| 12 | Linear OA(3218, 250, F3, 111) (dual of [250, 32, 112]-code) | [i] | ||
| 13 | Linear OA(3218, 250, F3, 110) (dual of [250, 32, 111]-code) | [i] | ||
| 14 | Linear OA(3218, 250, F3, 109) (dual of [250, 32, 110]-code) | [i] | ||
| 15 | Linear OA(3218, 250, F3, 108) (dual of [250, 32, 109]-code) | [i] | ||
| 16 | Linear OA(3218, 250, F3, 107) (dual of [250, 32, 108]-code) | [i] | ||
| 17 | Linear OA(3222, 254, F3, 123) (dual of [254, 32, 124]-code) | [i] | Code Embedding in Larger Space | |
| 18 | Linear OA(3223, 255, F3, 123) (dual of [255, 32, 124]-code) | [i] | ||
| 19 | Linear OA(3250, 282, F3, 123) (dual of [282, 32, 124]-code) | [i] | ||
| 20 | Linear OA(3236, 269, F3, 123) (dual of [269, 33, 124]-code) | [i] | Construction X with Varšamov Bound | |
| 21 | Linear OA(3244, 278, F3, 123) (dual of [278, 34, 124]-code) | [i] | ||
| 22 | Linear OA(3247, 282, F3, 123) (dual of [282, 35, 124]-code) | [i] | ||
| 23 | Linear OA(3249, 285, F3, 123) (dual of [285, 36, 124]-code) | [i] | ||
| 24 | Linear OOA(3218, 125, F3, 2, 123) (dual of [(125, 2), 32, 124]-NRT-code) | [i] | OOA Folding | |
| 25 | Linear OOA(3218, 83, F3, 3, 123) (dual of [(83, 3), 31, 124]-NRT-code) | [i] | ||
| 26 | Linear OOA(3218, 50, F3, 5, 123) (dual of [(50, 5), 32, 124]-NRT-code) | [i] | ||