Information on Result #701443
Linear OA(733, 52, F7, 21) (dual of [52, 19, 22]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,41}), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,41}) based on
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,41}, and minimum distance d ≥ |{−1,0,…,18}|+1 = 21 (BCH-bound) [i]
- linear OA(731, 48, F7, 20) (dual of [48, 17, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(733, 48, F7, 21) (dual of [48, 15, 22]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,41}, and minimum distance d ≥ |{−1,0,…,19}|+1 = 22 (BCH-bound) [i]
- linear OA(729, 48, F7, 19) (dual of [48, 19, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code) (see above)
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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(733, 26, F7, 2, 21) (dual of [(26, 2), 19, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(733, 17, F7, 3, 21) (dual of [(17, 3), 18, 22]-NRT-code) | [i] | ||