MinT - Information on Result #1538298

Information on Result #1538298

Linear OOA(4¹⁵⁷, 56073, F₄, 3, 24) (dual of [(56073, 3), 168062, 25]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁵⁷, 56073, F₄, 24) (dual of [56073, 55916, 25]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁵⁷, 65588, F₄, 24) (dual of [65588, 65431, 25]-code), using
- 1 times truncation [i] based on linear OA(4¹⁵⁸, 65589, F₄, 25) (dual of [65589, 65431, 26]-code), using
  - constructionÂ X applied to C_e(24) âŠ‚ C_e(17) [i] based on
    1. linear OA(4¹⁴⁵, 65536, F₄, 25) (dual of [65536, 65391, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [i]
    2. linear OA(4¹⁰⁵, 65536, F₄, 18) (dual of [65536, 65431, 19]-code), using an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]
    3. linear OA(4¹³, 53, F₄, 6) (dual of [53, 40, 7]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹³, 63, F₄, 6) (dual of [63, 50, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [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(4¹⁵⁷, 14018, F₄, 27, 24) (dual of [(14018, 27), 378329, 25]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row