MinT - Information on Result #636691

Information on Result #636691

Linear OA(4¹¹⁰, 155, F₄, 50) (dual of [155, 45, 51]-code), using concatenation of two codes based on

linear OA(64¹⁶, 31, F₆₄, 16) (dual of [31, 15, 17]-code or 31-arc in PG(15,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁶, 64, F₆₄, 16) (dual of [64, 48, 17]-code or 64-arc in PG(15,64)), using
  - Reedâ€“Solomon code RS(48,64) [i]
linear OA(4², 5, F₄, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reedâ€“Solomon code RS_e(3,4) [i]
- Hamming code H(2,4) [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(4¹¹⁰, 155, F₄, 49) (dual of [155, 45, 50]-code)	[i]		Strength Reduction
2	Linear OA(4¹¹¹, 156, F₄, 50) (dual of [156, 45, 51]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹⁰⁹, 154, F₄, 49) (dual of [154, 45, 50]-code)	[i]		Truncation
4	Linear OA(4¹⁰⁸, 153, F₄, 48) (dual of [153, 45, 49]-code)	[i]		Truncation
5	Linear OOA(4¹¹⁰, 77, F₄, 2, 50) (dual of [(77, 2), 44, 51]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹¹⁰, 51, F₄, 3, 50) (dual of [(51, 3), 43, 51]-NRT-code)	[i]		OOA Folding