Information on Result #2282363
Linear OA(8172, 550, F8, 61) (dual of [550, 378, 62]-code), using 1 times code embedding in larger space based on linear OA(8171, 549, F8, 61) (dual of [549, 378, 62]-code), using
- construction XX applied to C1 = C([25,81]), C2 = C([21,75]), C3 = C1 + C2 = C([25,75]), and C∩ = C1 ∩ C2 = C([21,81]) [i] based on
- linear OA(8148, 511, F8, 57) (dual of [511, 363, 58]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {25,26,…,81}, and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(8145, 511, F8, 55) (dual of [511, 366, 56]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {21,22,…,75}, and designed minimum distance d ≥ |I|+1 = 56 [i]
- linear OA(8160, 511, F8, 61) (dual of [511, 351, 62]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {21,22,…,81}, and designed minimum distance d ≥ |I|+1 = 62 [i]
- linear OA(8133, 511, F8, 51) (dual of [511, 378, 52]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {25,26,…,75}, and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(87, 22, F8, 5) (dual of [22, 15, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(87, 57, F8, 5) (dual of [57, 50, 6]-code), using
- linear OA(84, 16, F8, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,8)), 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 OOA(8172, 275, F8, 2, 61) (dual of [(275, 2), 378, 62]-NRT-code) | [i] | OOA Folding | |