Information on Result #2183996
Linear OA(2203, 219, F2, 93) (dual of [219, 16, 94]-code), using strength reduction based on linear OA(2203, 219, F2, 95) (dual of [219, 16, 96]-code), using
- concatenation of two codes [i] based on
- linear OA(465, 73, F4, 47) (dual of [73, 8, 48]-code), using
- construction XX applied to C1 = C([0,125]), C2 = C([1,140]), C3 = C1 + C2 = C([1,125]), and C∩ = C1 ∩ C2 = C([0,140]) [i] based on
- linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using contraction [i] based on linear OA(4182, 189, F4, 128) (dual of [189, 7, 129]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,125], and minimum distance d ≥ |{−2,−1,…,125}|+1 = 129 (BCH-bound) [i]
- linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using contraction [i] based on linear OA(4185, 189, F4, 140) (dual of [189, 4, 141]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,140], and designed minimum distance d ≥ |I|+1 = 141 [i]
- linear OA(460, 63, F4, 47) (dual of [63, 3, 48]-code), using contraction [i] based on linear OA(4186, 189, F4, 143) (dual of [189, 3, 144]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,140], and minimum distance d ≥ |{−7,−2,3,…,−53}|+1 = 144 (BCH-bound) [i]
- linear OA(455, 63, F4, 41) (dual of [63, 8, 42]-code), using contraction [i] based on linear OA(4181, 189, F4, 125) (dual of [189, 8, 126]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,125], and designed minimum distance d ≥ |I|+1 = 126 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(45, 9, F4, 4) (dual of [9, 4, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(45, 11, F4, 4) (dual of [11, 6, 5]-code), using
- construction XX applied to C1 = C([0,125]), C2 = C([1,140]), C3 = C1 + C2 = C([1,125]), and C∩ = C1 ∩ C2 = C([0,140]) [i] based on
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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(465, 73, F4, 47) (dual of [73, 8, 48]-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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2202, 218, F2, 92) (dual of [218, 16, 93]-code) | [i] | Truncation | |
| 2 | Linear OA(2199, 215, F2, 89) (dual of [215, 16, 90]-code) | [i] | ||
| 3 | Linear OA(2198, 214, F2, 88) (dual of [214, 16, 89]-code) | [i] | ||