MinT - Information on Result #638102

Information on Result #638102

Linear OA(5¹⁰¹, 115, F₅, 67) (dual of [115, 14, 68]-code), using concatenation of two codes based on

linear OA(25¹⁶, 23, F₂₅, 16) (dual of [23, 7, 17]-code or 23-arc in PG(15,25)), using
- discarding factors / shortening the dual code based on linear OA(25¹⁶, 25, F₂₅, 16) (dual of [25, 9, 17]-code or 25-arc in PG(15,25)), using
  - Reedâ€“Solomon code RS(9,25) [i]
linear OA(5³, 5, F₅, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,5) or 5-cap in PG(2,5)), using
- Reedâ€“Solomon code RS(2,5) [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(5¹⁰¹, 115, F₅, 66) (dual of [115, 14, 67]-code)	[i]		Strength Reduction
2	Linear OA(5¹⁰¹, 115, F₅, 65) (dual of [115, 14, 66]-code)	[i]		Strength Reduction
3	Linear OA(5¹⁰⁰, 114, F₅, 66) (dual of [114, 14, 67]-code)	[i]		Truncation
4	Linear OA(5⁹⁹, 113, F₅, 65) (dual of [113, 14, 66]-code)	[i]
5	Linear OA(5⁹⁸, 112, F₅, 64) (dual of [112, 14, 65]-code)	[i]
6	Linear OA(5⁹⁷, 111, F₅, 63) (dual of [111, 14, 64]-code)	[i]
7	Linear OA(5⁹⁵, 109, F₅, 61) (dual of [109, 14, 62]-code)	[i]
8	Linear OA(5⁹⁴, 108, F₅, 60) (dual of [108, 14, 61]-code)	[i]
9	Linear OA(5⁹³, 107, F₅, 59) (dual of [107, 14, 60]-code)	[i]
10	Linear OA(5⁹², 106, F₅, 58) (dual of [106, 14, 59]-code)	[i]
11	Linear OA(5⁹¹, 105, F₅, 57) (dual of [105, 14, 58]-code)	[i]
12	Linear OOA(5¹⁰¹, 57, F₅, 2, 67) (dual of [(57, 2), 13, 68]-NRT-code)	[i]		OOA Folding
13	Linear OOA(5¹⁰¹, 38, F₅, 3, 67) (dual of [(38, 3), 13, 68]-NRT-code)	[i]		OOA Folding