MinT - Information on Result #662099

Information on Result #662099

Linear OA(3¹², 56, F₃, 5) (dual of [56, 44, 6]-code), using (u,Â u+v)-construction based on

linear OA(3⁴, 28, F₃, 2) (dual of [28, 24, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(3⁴, 40, F₃, 2) (dual of [40, 36, 3]-code), using
  - Hamming code H(4,3) [i]
linear OA(3⁸, 28, F₃, 5) (dual of [28, 20, 6]-code), using
- dual code (with bound on d by constructionÂ Y1) [i] based on
  1. linear OA(3²⁰, 28, F₃, 14) (dual of [28, 8, 15]-code), using
    - contraction [i] based on linear OA(3⁴⁸, 56, F₃, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56Â | 3⁶âˆ’1, defining interval IÂ =Â {0,1,…,28}, and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
  2. nonexistence of linear OA(3¹⁹, 23, F₃, 14) (dual of [23, 4, 15]-code), because
    - 2 times truncation [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
      - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]

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		Method
1	Linear OA(3²³⁷, 4783026, F₃, 25) (dual of [4783026, 4782789, 26]-code)	[i]	ConstructionÂ X with Cyclic Codes
2	Linear OA(3²⁰⁹, 4783026, F₃, 21) (dual of [4783026, 4782817, 22]-code)	[i]
3	Linear OA(3²⁴⁷, 1594380, F₃, 27) (dual of [1594380, 1594133, 28]-code)	[i]
4	Linear OA(3²²¹, 1594380, F₃, 25) (dual of [1594380, 1594159, 26]-code)	[i]
5	Linear OA(3¹⁹⁵, 1594380, F₃, 21) (dual of [1594380, 1594185, 22]-code)	[i]
6	Linear OA(3²²⁹, 531498, F₃, 27) (dual of [531498, 531269, 28]-code)	[i]
7	Linear OA(3²⁰⁵, 531498, F₃, 25) (dual of [531498, 531293, 26]-code)	[i]
8	Linear OA(3¹⁸¹, 531498, F₃, 21) (dual of [531498, 531317, 22]-code)	[i]
9	Linear OA(3²³³, 177204, F₃, 31) (dual of [177204, 176971, 32]-code)	[i]
10	Linear OA(3²¹¹, 177204, F₃, 27) (dual of [177204, 176993, 28]-code)	[i]
11	Linear OA(3¹⁸⁹, 177204, F₃, 25) (dual of [177204, 177015, 26]-code)	[i]
12	Linear OA(3¹⁶⁷, 177204, F₃, 21) (dual of [177204, 177037, 22]-code)	[i]
13	Linear OA(3²²³, 4783025, F₃, 23) (dual of [4783025, 4782802, 24]-code)	[i]	ConstructionÂ X with Extended Narrow-Sense BCH Codes
14	Linear OA(3²⁰⁹, 4783025, F₃, 22) (dual of [4783025, 4782816, 23]-code)	[i]
15	Linear OA(3¹⁹⁵, 4783025, F₃, 20) (dual of [4783025, 4782830, 21]-code)	[i]
16	Linear OA(3²⁴⁷, 1594379, F₃, 28) (dual of [1594379, 1594132, 29]-code)	[i]
17	Linear OA(3²³⁴, 1594379, F₃, 26) (dual of [1594379, 1594145, 27]-code)	[i]
18	Linear OA(3²⁰⁸, 1594379, F₃, 23) (dual of [1594379, 1594171, 24]-code)	[i]
19	Linear OA(3¹⁹⁵, 1594379, F₃, 22) (dual of [1594379, 1594184, 23]-code)	[i]
20	Linear OA(3¹⁸², 1594379, F₃, 20) (dual of [1594379, 1594197, 21]-code)	[i]
21	Linear OA(3²⁴¹, 531497, F₃, 29) (dual of [531497, 531256, 30]-code)	[i]
22	Linear OA(3²²⁹, 531497, F₃, 28) (dual of [531497, 531268, 29]-code)	[i]
23	Linear OA(3²¹⁷, 531497, F₃, 26) (dual of [531497, 531280, 27]-code)	[i]
24	Linear OA(3¹⁹³, 531497, F₃, 23) (dual of [531497, 531304, 24]-code)	[i]
25	Linear OA(3¹⁸¹, 531497, F₃, 22) (dual of [531497, 531316, 23]-code)	[i]
26	Linear OA(3¹⁶⁹, 531497, F₃, 20) (dual of [531497, 531328, 21]-code)	[i]
27	Linear OA(3²⁴⁴, 177203, F₃, 32) (dual of [177203, 176959, 33]-code)	[i]
28	Linear OA(3²²², 177203, F₃, 29) (dual of [177203, 176981, 30]-code)	[i]
29	Linear OA(3²¹¹, 177203, F₃, 28) (dual of [177203, 176992, 29]-code)	[i]
30	Linear OA(3²⁰⁰, 177203, F₃, 26) (dual of [177203, 177003, 27]-code)	[i]
31	Linear OA(3¹⁷⁸, 177203, F₃, 23) (dual of [177203, 177025, 24]-code)	[i]
32	Linear OA(3¹⁶⁷, 177203, F₃, 22) (dual of [177203, 177036, 23]-code)	[i]
33	Linear OA(3¹⁵⁶, 177203, F₃, 20) (dual of [177203, 177047, 21]-code)	[i]