Information on Result #705173
Linear OA(3179, 759, F3, 44) (dual of [759, 580, 45]-code), using construction XX applied to C1 = C([322,364]), C2 = C([327,365]), C3 = C1 + C2 = C([327,364]), and C∩ = C1 ∩ C2 = C([322,365]) based on
- linear OA(3166, 728, F3, 43) (dual of [728, 562, 44]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {322,323,…,364}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(3154, 728, F3, 39) (dual of [728, 574, 40]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {327,328,…,365}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(3172, 728, F3, 44) (dual of [728, 556, 45]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {322,323,…,365}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(3148, 728, F3, 38) (dual of [728, 580, 39]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {327,328,…,364}, and designed minimum distance d ≥ |I|+1 = 39 [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(3179, 379, F3, 2, 44) (dual of [(379, 2), 579, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(3179, 253, F3, 3, 44) (dual of [(253, 3), 580, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(3179, 189, F3, 4, 44) (dual of [(189, 4), 577, 45]-NRT-code) | [i] | ||