Information on Result #1662473
Linear OOA(293, 227, F2, 6, 21) (dual of [(227, 6), 1269, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(293, 227, F2, 2, 21) (dual of [(227, 2), 361, 22]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(293, 265, F2, 2, 21) (dual of [(265, 2), 437, 22]-NRT-code), using
- OOA 2-folding [i] based on linear OA(293, 530, F2, 21) (dual of [530, 437, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(293, 531, F2, 21) (dual of [531, 438, 22]-code), using
- construction XX applied to C1 = C([509,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([509,18]) [i] based on
- linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,16}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(282, 511, F2, 19) (dual of [511, 429, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(291, 511, F2, 21) (dual of [511, 420, 22]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,18}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
- construction XX applied to C1 = C([509,16]), C2 = C([0,18]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([509,18]) [i] based on
- discarding factors / shortening the dual code based on linear OA(293, 531, F2, 21) (dual of [531, 438, 22]-code), using
- OOA 2-folding [i] based on linear OA(293, 530, F2, 21) (dual of [530, 437, 22]-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.