Information on Result #1310807
Linear OA(591, 657, F5, 28) (dual of [657, 566, 29]-code), using 23 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 12 times 0) based on linear OA(587, 630, F5, 28) (dual of [630, 543, 29]-code), using
- construction XX applied to C1 = C([623,25]), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([623,26]) [i] based on
- linear OA(585, 624, F5, 27) (dual of [624, 539, 28]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,25}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(587, 624, F5, 28) (dual of [624, 537, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(581, 624, F5, 26) (dual of [624, 543, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(591, 657, F5, 2, 28) (dual of [(657, 2), 1223, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(591, 657, F5, 3, 28) (dual of [(657, 3), 1880, 29]-NRT-code) | [i] | ||
| 3 | Digital (63, 91, 657)-net over F5 | [i] | ||
| 4 | Linear OOA(591, 328, F5, 2, 28) (dual of [(328, 2), 565, 29]-NRT-code) | [i] | OOA Folding | |