Information on Result #1479802
Linear OOA(4207, 27327, F4, 3, 32) (dual of [(27327, 3), 81774, 33]-NRT-code), using OOA 2-folding based on linear OOA(4207, 54654, F4, 2, 32) (dual of [(54654, 2), 109101, 33]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4207, 54654, F4, 32) (dual of [54654, 54447, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4207, 65599, F4, 32) (dual of [65599, 65392, 33]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4206, 65598, F4, 32) (dual of [65598, 65392, 33]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(4193, 65537, F4, 33) (dual of [65537, 65344, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(413, 61, F4, 6) (dual of [61, 48, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4206, 65598, F4, 32) (dual of [65598, 65392, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(4207, 65599, F4, 32) (dual of [65599, 65392, 33]-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.