Information on Result #710896
Linear OA(540, 639, F5, 12) (dual of [639, 599, 13]-code), using construction XX applied to C1 = C([146,156]), C2 = C([149,157]), C3 = C1 + C2 = C([149,156]), and C∩ = C1 ∩ C2 = C([146,157]) based on
- linear OA(533, 624, F5, 11) (dual of [624, 591, 12]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,156}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(529, 624, F5, 9) (dual of [624, 595, 10]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {149,150,…,157}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(537, 624, F5, 12) (dual of [624, 587, 13]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {146,147,…,157}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(525, 624, F5, 8) (dual of [624, 599, 9]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {149,150,…,156}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(53, 11, F5, 2) (dual of [11, 8, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- 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
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(540, 319, F5, 2, 12) (dual of [(319, 2), 598, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(540, 213, F5, 3, 12) (dual of [(213, 3), 599, 13]-NRT-code) | [i] | ||