Information on Result #1669513
Linear OOA(2223, 2097416, F2, 6, 16) (dual of [(2097416, 6), 12584273, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2223, 2097416, F2, 4, 16) (dual of [(2097416, 4), 8389441, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(239, 266, F2, 4, 8) (dual of [(266, 4), 1025, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(239, 266, F2, 2, 8) (dual of [(266, 2), 493, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- linear OA(228, 511, F2, 7) (dual of [511, 483, 8]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(227, 511, F2, 6) (dual of [511, 484, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(237, 511, F2, 9) (dual of [511, 474, 10]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(218, 511, F2, 4) (dual of [511, 493, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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), 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 (see above)
- construction XX applied to C1 = C([509,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([509,6]) [i] based on
- OOA 2-folding [i] based on linear OA(239, 532, F2, 8) (dual of [532, 493, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(239, 266, F2, 2, 8) (dual of [(266, 2), 493, 9]-NRT-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(239, 266, F2, 4, 8) (dual of [(266, 4), 1025, 9]-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.
Other Results with Identical Parameters
None.
Depending Results
None.