MinT - Information on Result #738061

Information on Result #738061

Linear OA(2²¹⁷, 231, F₂, 103) (dual of [231, 14, 104]-code), using concatenation of two codes based on

linear OA(4⁷⁰, 77, F₄, 51) (dual of [77, 7, 52]-code), using
- BCH codes lengthened with UEP codes [i]
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
  - parity-check code [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		This result only	Method
1	Linear OA(2²¹⁷, 231, F₂, 102) (dual of [231, 14, 103]-code)	[i]		Strength Reduction
2	Linear OA(2²¹⁷, 231, F₂, 101) (dual of [231, 14, 102]-code)	[i]
3	Linear OA(2²¹⁷, 231, F₂, 100) (dual of [231, 14, 101]-code)	[i]
4	Linear OA(2²¹⁸, 232, F₂, 103) (dual of [232, 14, 104]-code)	[i]		Code Embedding in Larger Space
5	Linear OA(2²¹⁹, 233, F₂, 103) (dual of [233, 14, 104]-code)	[i]
6	Linear OA(2²²⁰, 234, F₂, 103) (dual of [234, 14, 104]-code)	[i]
7	Linear OA(2²¹⁶, 230, F₂, 102) (dual of [230, 14, 103]-code)	[i]		Truncation
8	Linear OA(2²¹⁵, 229, F₂, 101) (dual of [229, 14, 102]-code)	[i]
9	Linear OA(2²¹⁴, 228, F₂, 100) (dual of [228, 14, 101]-code)	[i]
10	Linear OA(2²¹³, 227, F₂, 99) (dual of [227, 14, 100]-code)	[i]
11	Linear OA(2²¹², 226, F₂, 98) (dual of [226, 14, 99]-code)	[i]
12	Linear OA(2²¹⁰, 224, F₂, 96) (dual of [224, 14, 97]-code)	[i]
13	Linear OOA(2²¹⁷, 115, F₂, 2, 103) (dual of [(115, 2), 13, 104]-NRT-code)	[i]		OOA Folding
14	Linear OOA(2²¹⁷, 77, F₂, 3, 103) (dual of [(77, 3), 14, 104]-NRT-code)	[i]
15	Linear OOA(2²¹⁷, 46, F₂, 5, 103) (dual of [(46, 5), 13, 104]-NRT-code)	[i]