MinT - Information on Result #2417399

Information on Result #2417399

Linear OOA(2⁷², 38, F₂, 2, 48) (dual of [(38, 2), 4, 49]-NRT-code), using strength reduction based on linear OOA(2⁷², 38, F₂, 2, 49) (dual of [(38, 2), 4, 50]-NRT-code), using

juxtaposition [i] based on
1. linear OOA(2¹², 8, F₂, 2, 9) (dual of [(8, 2), 4, 10]-NRT-code), using
  - an explicit generator matrix by Edel [i]
2. linear OOA(2⁵⁶, 30, F₂, 2, 39) (dual of [(30, 2), 4, 40]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(4⁸, 10, F₄, 7) (dual of [10, 2, 8]-code), using
      - repeating each code word 2 times [i] based on linear OA(4³, 5, F₄, 3) (dual of [5, 2, 4]-code or 5-arc in PG(2,4) or 5-cap in PG(2,4)), using
        extended Reedâ€“Solomon code RS_e(2,4) [i]
        Simplex code S(2,4) [i]
    2. linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
      - extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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(2⁷², 19, F₂, 4, 48) (dual of [(19, 4), 4, 49]-NRT-code)	[i]		OOA Folding