Information on Result #712335
Linear OA(5143, 656, F5, 43) (dual of [656, 513, 44]-code), using construction XX applied to C1 = C([619,35]), C2 = C([0,37]), C3 = C1 + C2 = C([0,35]), and C∩ = C1 ∩ C2 = C([619,37]) based on
- linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,35}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5135, 624, F5, 43) (dual of [624, 489, 44]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−5,−4,…,37}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,35], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(57, 23, F5, 4) (dual of [23, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(57, 24, F5, 4) (dual of [24, 17, 5]-code), using
- linear OA(51, 9, F5, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 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 OOA(5143, 328, F5, 2, 43) (dual of [(328, 2), 513, 44]-NRT-code) | [i] | OOA Folding | |