MinT - Information on Result #2629402

Information on Result #2629402

Linear OOA(4⁵⁰, large, F₄, 3, 4), using strength reduction based on linear OOA(4⁵⁰, large, F₄, 3, 5), using

(u,Â u+v)-construction [i] based on
1. linear OOA(4², 5, F₄, 3, 2) (dual of [(5, 3), 13, 3]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(3;13,4) [i]
2. linear OOA(4⁴⁸, 8388602, F₄, 3, 5) (dual of [(8388602, 3), 25165758, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(4⁴⁸, large, F₄, 2, 5), using
    - generalized (u,Â u+v)-construction [i] based on
      1. linear OOA(4¹, 2097152, F₄, 2, 1) (dual of [(2097152, 2), 4194303, 2]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4¹, s, F₄, 2, 1) for arbitrarily large s, using
        appending 1 arbitrary column [i] based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
      2. linear OOA(4¹, 2097152, F₄, 2, 1) (dual of [(2097152, 2), 4194303, 2]-NRT-code) (see above)
      3. linear OOA(4¹², 2097152, F₄, 2, 2) (dual of [(2097152, 2), 4194292, 3]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(4¹², 5592405, F₄, 2, 2) (dual of [(5592405, 2), 11184798, 3]-NRT-code), using
        appending kth column [i] based on linear OA(4¹², 5592405, F₄, 2) (dual of [5592405, 5592393, 3]-code), using
        Hamming code H(12,4) [i]
      4. linear OOA(4³⁴, 2097152, F₄, 2, 5) (dual of [(2097152, 2), 4194270, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(4³⁴, 4194304, F₄, 5) (dual of [4194304, 4194270, 6]-code), using
        an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 4194303Â = 4¹¹âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m 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(4⁵¹, large, F₄, 3, 4)	[i]		OOA Duplication
2	Linear OOA(4⁵², large, F₄, 3, 4)	[i]		OOA Duplication