MinT - Information on Result #2448584

Information on Result #2448584

Linear OOA(5¹⁵⁰, 77, F₅, 2, 125) (dual of [(77, 2), 4, 126]-NRT-code), using strength reduction based on linear OOA(5¹⁵⁰, 77, F₅, 2, 126) (dual of [(77, 2), 4, 127]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(5⁴, 4, F₅, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(5⁴, 5, F₅, 2, 4) (dual of [(5, 2), 6, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;6,5) [i]
2. linear OOA(5¹⁴², 73, F₅, 2, 121) (dual of [(73, 2), 4, 122]-NRT-code), using
  - 4 step truncation [i] based on linear OOA(5¹⁴⁶, 75, F₅, 2, 125) (dual of [(75, 2), 4, 126]-NRT-code), using
    - concatenation of two NRT-codes [i] based on
      1. linear OA(25¹³, 15, F₂₅, 13) (dual of [15, 2, 14]-code or 15-arc in PG(12,25)), using
        discarding factors / shortening the dual code based on linear OA(25¹³, 25, F₂₅, 13) (dual of [25, 12, 14]-code or 25-arc in PG(12,25)), using
        Reedâ€“Solomon code RS(12,25) [i]
      2. linear OOA(5⁸, 5, F₅, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
        Reedâ€“Solomon NRT-code RS(2;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		This result only	Method
1	Linear OOA(5¹³⁸, 71, F₅, 2, 113) (dual of [(71, 2), 4, 114]-NRT-code)	[i]		Truncation for OOAs