MinT - Information on Result #636702

Information on Result #636702

Linear OA(4¹¹³, 155, F₄, 53) (dual of [155, 42, 54]-code), using concatenation of two codes based on

linear OA(64¹⁷, 31, F₆₄, 17) (dual of [31, 14, 18]-code or 31-arc in PG(16,64)), using
- discarding factors / shortening the dual code based on linear OA(64¹⁷, 64, F₆₄, 17) (dual of [64, 47, 18]-code or 64-arc in PG(16,64)), using
  - Reedâ€“Solomon code RS(47,64) [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(4¹¹³, 155, F₄, 52) (dual of [155, 42, 53]-code)	[i]		Strength Reduction
2	Linear OA(4¹¹⁴, 156, F₄, 53) (dual of [156, 42, 54]-code)	[i]		Code Embedding in Larger Space
3	Linear OA(4¹¹², 154, F₄, 52) (dual of [154, 42, 53]-code)	[i]		Truncation
4	Linear OA(4¹¹¹, 153, F₄, 51) (dual of [153, 42, 52]-code)	[i]		Truncation
5	Linear OOA(4¹¹³, 77, F₄, 2, 53) (dual of [(77, 2), 41, 54]-NRT-code)	[i]		OOA Folding
6	Linear OOA(4¹¹³, 51, F₄, 3, 53) (dual of [(51, 3), 40, 54]-NRT-code)	[i]		OOA Folding