MinT - Information on Result #1539963

Information on Result #1539963

Linear OOA(4¹⁸², 418667, F₄, 3, 24) (dual of [(418667, 3), 1255819, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁸², 418667, F₄, 2, 24) (dual of [(418667, 2), 837152, 25]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁸², 524298, F₄, 2, 24) (dual of [(524298, 2), 1048414, 25]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁸², 1048596, F₄, 24) (dual of [1048596, 1048414, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸², 1048597, F₄, 24) (dual of [1048597, 1048415, 25]-code), using
    - constructionÂ X applied to C_e(24) âŠ‚ C_e(21) [i] based on
      1. linear OA(4¹⁸¹, 1048576, F₄, 25) (dual of [1048576, 1048395, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
      2. linear OA(4¹⁶¹, 1048576, F₄, 22) (dual of [1048576, 1048415, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 4¹⁰âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. linear OA(4¹, 21, F₄, 1) (dual of [21, 20, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]

Mode: 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(4¹⁸², 104666, F₄, 27, 24) (dual of [(104666, 27), 2825800, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row