Information on Result #681989
Linear OA(463, 70, F4, 47) (dual of [70, 7, 48]-code), using construction XX applied to C1 = C([0,128]), C2 = C([1,140]), C3 = C1 + C2 = C([1,128]), and C∩ = C1 ∩ C2 = C([0,140]) based on
- linear OA(457, 63, F4, 43) (dual of [63, 6, 44]-code), using contraction [i] based on linear OA(4183, 189, F4, 131) (dual of [189, 6, 132]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,128], and minimum distance d ≥ |{−2,−1,…,128}|+1 = 132 (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(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 narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,128], and designed minimum distance d ≥ |I|+1 = 129 [i]
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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(461, 68, F4, 45) (dual of [68, 7, 46]-code) | [i] | Truncation | |
| 2 | Linear OA(460, 67, F4, 44) (dual of [67, 7, 45]-code) | [i] | ||
| 3 | Linear OA(4133, 140, F4, 95) (dual of [140, 7, 96]-code) | [i] | Repeating Each Code Word | |
| 4 | Linear OA(4124, 131, F4, 88) (dual of [131, 7, 89]-code) | [i] | Juxtaposition | |
| 5 | Linear OA(4125, 132, F4, 89) (dual of [132, 7, 90]-code) | [i] | ||
| 6 | Linear OA(4126, 133, F4, 90) (dual of [133, 7, 91]-code) | [i] | ||
| 7 | Linear OA(4127, 134, F4, 91) (dual of [134, 7, 92]-code) | [i] | ||
| 8 | Linear OA(4138, 145, F4, 98) (dual of [145, 7, 99]-code) | [i] | ||
| 9 | Linear OA(2196, 210, F2, 95) (dual of [210, 14, 96]-code) | [i] | Concatenation of Two Codes | |
| 10 | Linear OOA(463, 35, F4, 2, 47) (dual of [(35, 2), 7, 48]-NRT-code) | [i] | OOA Folding | |