Information on Result #707403
Linear OA(4221, 1092, F4, 53) (dual of [1092, 871, 54]-code), using construction X applied to C([0,52]) ⊂ C([0,40]) based on
- linear OA(4196, 1023, F4, 53) (dual of [1023, 827, 54]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,52], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(425, 69, F4, 11) (dual of [69, 44, 12]-code), using
- construction XX applied to C1 = C({0,1,2,3,5,6,7,47}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,47}) [i] based on
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,47}, and minimum distance d ≥ |{−1,0,…,8}|+1 = 11 (BCH-bound) [i]
- linear OA(422, 63, F4, 10) (dual of [63, 41, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(425, 63, F4, 11) (dual of [63, 38, 12]-code), using the primitive cyclic code C(A) with length 63 = 43−1, defining set A = {0,1,2,3,5,6,7,9,47}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
- linear OA(419, 63, F4, 9) (dual of [63, 44, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(40, 3, F4, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,3,5,6,7,47}), C2 = C([0,9]), C3 = C1 + C2 = C([0,7]), and C∩ = C1 ∩ C2 = C({0,1,2,3,5,6,7,9,47}) [i] based on
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(4221, 546, F4, 2, 53) (dual of [(546, 2), 871, 54]-NRT-code) | [i] | OOA Folding | |