MinT - Information on Result #1540828

Information on Result #1540828

Linear OOA(4¹⁹⁴, 28608, F₄, 3, 33) (dual of [(28608, 3), 85630, 34]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4¹⁹⁴, 28608, F₄, 2, 33) (dual of [(28608, 2), 57022, 34]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4¹⁹⁴, 32772, F₄, 2, 33) (dual of [(32772, 2), 65350, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4¹⁹⁴, 65544, F₄, 33) (dual of [65544, 65350, 34]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁹⁴, 65545, F₄, 33) (dual of [65545, 65351, 34]-code), using
    - constructionÂ X applied to C_e(32) âŠ‚ C_e(30) [i] based on
      1. linear OA(4¹⁹³, 65536, F₄, 33) (dual of [65536, 65343, 34]-code), using an extension C_e(32) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,32], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 33 [i]
      2. linear OA(4¹⁸⁵, 65536, F₄, 31) (dual of [65536, 65351, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
      3. linear OA(4¹, 9, F₄, 1) (dual of [9, 8, 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(4¹⁹⁴, 4767, F₄, 39, 33) (dual of [(4767, 39), 185719, 34]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row