Information on Result #1719370
Digital (122, 147, 7006)-net over F4, using net defined by OOA based on linear OOA(4147, 7006, F4, 27, 25) (dual of [(7006, 27), 189015, 26]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4147, 28025, F4, 3, 25) (dual of [(28025, 3), 83928, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 28028, F4, 3, 25) (dual of [(28028, 3), 83937, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4147, 28028, F4, 2, 25) (dual of [(28028, 2), 55909, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 32773, F4, 2, 25) (dual of [(32773, 2), 65399, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4147, 65546, F4, 25) (dual of [65546, 65399, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4147, 65547, F4, 25) (dual of [65547, 65400, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(41, 10, F4, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(24) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4147, 65547, F4, 25) (dual of [65547, 65400, 26]-code), using
- OOA 2-folding [i] based on linear OA(4147, 65546, F4, 25) (dual of [65546, 65399, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 32773, F4, 2, 25) (dual of [(32773, 2), 65399, 26]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4147, 28028, F4, 2, 25) (dual of [(28028, 2), 55909, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4147, 28028, F4, 3, 25) (dual of [(28028, 3), 83937, 26]-NRT-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.