Information on Result #1312060
Linear OA(831, 538, F8, 11) (dual of [538, 507, 12]-code), using 18 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 0, 1, 13 times 0) based on linear OA(828, 517, F8, 11) (dual of [517, 489, 12]-code), using
- construction XX applied to C1 = C([510,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([510,9]) [i] based on
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,8}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(825, 511, F8, 10) (dual of [511, 486, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(828, 511, F8, 11) (dual of [511, 483, 12]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(822, 511, F8, 9) (dual of [511, 489, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code) (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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(831, 538, F8, 2, 11) (dual of [(538, 2), 1045, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(831, 538, F8, 3, 11) (dual of [(538, 3), 1583, 12]-NRT-code) | [i] | ||
| 3 | Digital (20, 31, 538)-net over F8 | [i] | ||
| 4 | Linear OOA(831, 269, F8, 2, 11) (dual of [(269, 2), 507, 12]-NRT-code) | [i] | OOA Folding | |