MinT - Information on Result #1537402

Information on Result #1537402

Linear OOA(4¹⁴², 2333129, F₄, 3, 16) (dual of [(2333129, 3), 6999245, 17]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OA(4¹⁴², 2333129, F₄, 16) (dual of [2333129, 2332987, 17]-code), using

discarding factors / shortening the dual code based on linear OA(4¹⁴², 4194358, F₄, 16) (dual of [4194358, 4194216, 17]-code), using
- 1 times truncation [i] based on linear OA(4¹⁴³, 4194359, F₄, 17) (dual of [4194359, 4194216, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,5]) [i] based on
    1. linear OA(4¹³³, 4194305, F₄, 17) (dual of [4194305, 4194172, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(4⁸⁹, 4194305, F₄, 11) (dual of [4194305, 4194216, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305Â | 4²²âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (BCH-bound) [i]
    3. linear OA(4¹⁰, 54, F₄, 5) (dual of [54, 44, 6]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁰, 63, F₄, 5) (dual of [63, 53, 6]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 63Â = 4³âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [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(4¹⁴², 777709, F₄, 21, 16) (dual of [(777709, 21), 16331747, 17]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row