Information on Result #1622773
Linear OOA(3206, 961, F3, 5, 43) (dual of [(961, 5), 4599, 44]-NRT-code), using OOA 2-folding based on linear OOA(3206, 1922, F3, 3, 43) (dual of [(1922, 3), 5560, 44]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3206, 1923, F3, 3, 43) (dual of [(1923, 3), 5563, 44]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3206, 1923, F3, 43) (dual of [1923, 1717, 44]-code), using
- discarding factors / shortening the dual code based on linear OA(3206, 2218, F3, 43) (dual of [2218, 2012, 44]-code), using
- construction XX applied to Ce(42) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- linear OA(3197, 2187, F3, 43) (dual of [2187, 1990, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(3176, 2187, F3, 38) (dual of [2187, 2011, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3169, 2187, F3, 37) (dual of [2187, 2018, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2186 = 37−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(38, 30, F3, 4) (dual of [30, 22, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- the narrow-sense BCH-code C(I) with length 41 | 38−1, defining interval I = [1,1], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(38, 41, F3, 4) (dual of [41, 33, 5]-code), using
- linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(42) ⊂ Ce(37) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(3206, 2218, F3, 43) (dual of [2218, 2012, 44]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3206, 1923, F3, 43) (dual of [1923, 1717, 44]-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
None.