Information on Result #901914
Linear OOA(3231, 559, F32, 2, 12) (dual of [(559, 2), 1087, 13]-NRT-code), using (u, u+v)-construction based on
- linear OOA(327, 44, F32, 2, 6) (dual of [(44, 2), 81, 7]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,81P) [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- linear OOA(3224, 515, F32, 2, 12) (dual of [(515, 2), 1006, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3224, 1030, F32, 12) (dual of [1030, 1006, 13]-code), using
- construction XX applied to C1 = C([1021,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1021,9]) [i] based on
- linear OA(3221, 1023, F32, 11) (dual of [1023, 1002, 12]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3219, 1023, F32, 10) (dual of [1023, 1004, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(3223, 1023, F32, 12) (dual of [1023, 1000, 13]-code), using the primitive BCH-code C(I) with length 1023 = 322−1, defining interval I = {−2,−1,…,9}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(3217, 1023, F32, 9) (dual of [1023, 1006, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- Reed–Solomon code RS(31,32) [i]
- discarding factors / shortening the dual code based on linear OA(321, 32, F32, 1) (dual of [32, 31, 2]-code), using
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction XX applied to C1 = C([1021,8]), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C([1021,9]) [i] based on
- OOA 2-folding [i] based on linear OA(3224, 1030, F32, 12) (dual of [1030, 1006, 13]-code), using
Mode: Constructive and 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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3231, 186, F32, 14, 12) (dual of [(186, 14), 2573, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |