Information on Result #705312
Linear OA(3191, 759, F3, 47) (dual of [759, 568, 48]-code), using construction XX applied to C1 = C([319,364]), C2 = C([324,365]), C3 = C1 + C2 = C([324,364]), and C∩ = C1 ∩ C2 = C([319,365]) based on
- linear OA(3178, 728, F3, 46) (dual of [728, 550, 47]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {319,320,…,364}, and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(3166, 728, F3, 42) (dual of [728, 562, 43]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {324,325,…,365}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3184, 728, F3, 47) (dual of [728, 544, 48]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {319,320,…,365}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(3160, 728, F3, 41) (dual of [728, 568, 42]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {324,325,…,364}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(37, 25, F3, 4) (dual of [25, 18, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 5 [i]
- discarding factors / shortening the dual code based on linear OA(37, 26, F3, 4) (dual of [26, 19, 5]-code), using
- linear OA(30, 6, F3, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 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(3191, 379, F3, 2, 47) (dual of [(379, 2), 567, 48]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3191, 253, F3, 3, 47) (dual of [(253, 3), 568, 48]-NRT-code) | [i] | ||
| 3 | Linear OOA(3191, 189, F3, 4, 47) (dual of [(189, 4), 565, 48]-NRT-code) | [i] | ||