MinT - Information on Result #637278

Information on Result #637278

Linear OA(4¹⁴⁷, 174, F₄, 83) (dual of [174, 27, 84]-code), using concatenation of two codes based on

linear OA(64²⁰, 29, F₆₄, 20) (dual of [29, 9, 21]-code or 29-arc in PG(19,64)), using
- discarding factors / shortening the dual code based on linear OA(64²⁰, 64, F₆₄, 20) (dual of [64, 44, 21]-code or 64-arc in PG(19,64)), using
  - Reedâ€“Solomon code RS(44,64) [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
- hyperoval in PG(2,Â 4) [i]
- the Hexacode [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(4¹⁴⁷, 174, F₄, 82) (dual of [174, 27, 83]-code)	[i]		Strength Reduction
2	Linear OA(4¹⁴⁷, 174, F₄, 81) (dual of [174, 27, 82]-code)	[i]		Strength Reduction
3	Linear OA(4¹⁴⁸, 175, F₄, 83) (dual of [175, 27, 84]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4¹⁴⁶, 173, F₄, 82) (dual of [173, 27, 83]-code)	[i]		Truncation
5	Linear OA(4¹⁴⁵, 172, F₄, 81) (dual of [172, 27, 82]-code)	[i]
6	Linear OA(4¹⁴⁴, 171, F₄, 80) (dual of [171, 27, 81]-code)	[i]
7	Linear OA(4¹⁴³, 170, F₄, 79) (dual of [170, 27, 80]-code)	[i]
8	Linear OA(4¹⁴², 169, F₄, 78) (dual of [169, 27, 79]-code)	[i]
9	Linear OA(4¹⁴⁰, 167, F₄, 76) (dual of [167, 27, 77]-code)	[i]
10	Linear OOA(4¹⁴⁷, 87, F₄, 2, 83) (dual of [(87, 2), 27, 84]-NRT-code)	[i]		OOA Folding
11	Linear OOA(4¹⁴⁷, 58, F₄, 3, 83) (dual of [(58, 3), 27, 84]-NRT-code)	[i]		OOA Folding