MinT - Information on Result #2194177

Information on Result #2194177

Linear OA(3¹⁶⁸, 180, F₃, 100) (dual of [180, 12, 101]-code), using strength reduction based on linear OA(3¹⁶⁸, 180, F₃, 101) (dual of [180, 12, 102]-code), using

concatenation of two codes [i] based on
1. linear OA(27¹⁶, 20, F₂₇, 16) (dual of [20, 4, 17]-code or 20-arc in PG(15,27)), using
  - discarding factors / shortening the dual code based on linear OA(27¹⁶, 27, F₂₇, 16) (dual of [27, 11, 17]-code or 27-arc in PG(15,27)), using
    - Reedâ€“Solomon code RS(11,27) [i]
2. linear OA(3⁶, 9, F₃, 5) (dual of [9, 3, 6]-code), using
  - discarding factors / shortening the dual code based on linear OA(3⁶, 10, F₃, 5) (dual of [10, 4, 6]-code), using
    - projective code from ovoid in PG(3,Â 3) [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		Method
1	Linear OA(3¹⁶⁷, 179, F₃, 99) (dual of [179, 12, 100]-code)	[i]	Truncation
2	Linear OA(3¹⁶⁶, 178, F₃, 98) (dual of [178, 12, 99]-code)	[i]
3	Linear OA(3¹⁶⁵, 177, F₃, 97) (dual of [177, 12, 98]-code)	[i]
4	Linear OA(3¹⁶⁴, 176, F₃, 96) (dual of [176, 12, 97]-code)	[i]
5	Linear OA(3¹⁶³, 175, F₃, 95) (dual of [175, 12, 96]-code)	[i]
6	Linear OA(3¹⁶², 174, F₃, 94) (dual of [174, 12, 95]-code)	[i]
7	Linear OA(3¹⁶¹, 173, F₃, 93) (dual of [173, 12, 94]-code)	[i]
8	Linear OA(3¹⁶⁰, 172, F₃, 92) (dual of [172, 12, 93]-code)	[i]
9	Linear OA(3¹⁵⁸, 170, F₃, 90) (dual of [170, 12, 91]-code)	[i]
10	Linear OOA(3¹⁶⁸, 90, F₃, 2, 100) (dual of [(90, 2), 12, 101]-NRT-code)	[i]	OOA Folding
11	Linear OOA(3¹⁶⁸, 60, F₃, 3, 100) (dual of [(60, 3), 12, 101]-NRT-code)	[i]
12	Linear OOA(3¹⁶⁸, 36, F₃, 5, 100) (dual of [(36, 5), 12, 101]-NRT-code)	[i]