Information on Result #1441074
Linear OOA(751, 16829, F7, 2, 11) (dual of [(16829, 2), 33607, 12]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(751, 16829, F7, 11) (dual of [16829, 16778, 12]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(749, 16825, F7, 11) (dual of [16825, 16776, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(731, 16807, F7, 8) (dual of [16807, 16776, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(73, 18, F7, 2) (dual of [18, 15, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(73, 48, F7, 2) (dual of [48, 45, 3]-code), using
- construction X applied to Ce(10) ⊂ Ce(7) [i] based on
- linear OA(749, 16827, F7, 10) (dual of [16827, 16778, 11]-code), using Gilbert–Varšamov bound and bm = 749 > Vbs−1(k−1) = 2995 956949 232432 337061 320965 202951 521137 [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(749, 16825, F7, 11) (dual of [16825, 16776, 12]-code), using
Mode: 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(751, 8414, F7, 3, 11) (dual of [(8414, 3), 25191, 12]-NRT-code) | [i] | OOA Folding | |