MinT - Information on Result #2211348

Information on Result #2211348

Linear OA(5¹⁵⁰, 168, F₅, 93) (dual of [168, 18, 94]-code), using strength reduction based on linear OA(5¹⁵⁰, 168, F₅, 94) (dual of [168, 18, 95]-code), using

concatenation of two codes [i] based on
1. linear OA(25¹⁹, 28, F₂₅, 18) (dual of [28, 9, 19]-code), using
  - constructionÂ X applied to RS(7,25) âŠ‚ RS(9,25) [i] based on
    1. linear OA(25¹⁸, 25, F₂₅, 18) (dual of [25, 7, 19]-code or 25-arc in PG(17,25)), using Reedâ€“Solomon code RS(7,25) [i]
    2. 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]
    3. linear OA(25¹, 3, F₂₅, 1) (dual of [3, 2, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(25¹, s, F₂₅, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
2. linear OA(5⁴, 6, F₅, 4) (dual of [6, 2, 5]-code or 6-arc in PG(3,5)), using
  - extended Reedâ€“Solomon code RS_e(2,5) [i]
  - Simplex code S(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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OA(5¹⁴⁹, 167, F₅, 92) (dual of [167, 18, 93]-code)	[i]	Truncation
2	Linear OA(5¹⁴⁸, 166, F₅, 91) (dual of [166, 18, 92]-code)	[i]
3	Linear OA(5¹⁴⁷, 165, F₅, 90) (dual of [165, 18, 91]-code)	[i]
4	Linear OA(5¹⁴⁵, 163, F₅, 88) (dual of [163, 18, 89]-code)	[i]
5	Linear OA(5¹⁴⁴, 162, F₅, 87) (dual of [162, 18, 88]-code)	[i]
6	Linear OOA(5¹⁵⁰, 84, F₅, 2, 93) (dual of [(84, 2), 18, 94]-NRT-code)	[i]	OOA Folding
7	Linear OOA(5¹⁵⁰, 56, F₅, 3, 93) (dual of [(56, 3), 18, 94]-NRT-code)	[i]	OOA Folding