MinT - Information on Result #637248

Information on Result #637248

Linear OA(4¹¹⁷, 138, F₄, 67) (dual of [138, 21, 68]-code), using concatenation of two codes based on

linear OA(64¹⁶, 23, F₆₄, 16) (dual of [23, 7, 17]-code or 23-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(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(4¹¹⁷, 138, F₄, 66) (dual of [138, 21, 67]-code)	[i]		Strength Reduction
2	Linear OA(4¹¹⁷, 138, F₄, 65) (dual of [138, 21, 66]-code)	[i]		Strength Reduction
3	Linear OA(4¹¹⁸, 139, F₄, 67) (dual of [139, 21, 68]-code)	[i]		Code Embedding in Larger Space
4	Linear OA(4¹¹⁶, 137, F₄, 66) (dual of [137, 21, 67]-code)	[i]		Truncation
5	Linear OA(4¹¹⁵, 136, F₄, 65) (dual of [136, 21, 66]-code)	[i]
6	Linear OA(4¹¹⁴, 135, F₄, 64) (dual of [135, 21, 65]-code)	[i]
7	Linear OA(4¹¹³, 134, F₄, 63) (dual of [134, 21, 64]-code)	[i]
8	Linear OOA(4¹¹⁷, 69, F₄, 2, 67) (dual of [(69, 2), 21, 68]-NRT-code)	[i]		OOA Folding
9	Linear OOA(4¹¹⁷, 46, F₄, 3, 67) (dual of [(46, 3), 21, 68]-NRT-code)	[i]		OOA Folding