MinT - Information on Result #2274049

Information on Result #2274049

Linear OA(4¹⁵¹, 282, F₄, 53) (dual of [282, 131, 54]-code), using 1 times code embedding in larger space based on linear OA(4¹⁵⁰, 281, F₄, 53) (dual of [281, 131, 54]-code), using

constructionÂ X applied to C_e(52) âŠ‚ C_e(44) [i] based on
1. linear OA(4¹³⁹, 256, F₄, 53) (dual of [256, 117, 54]-code), using an extension C_e(52) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,52], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 53 [i]
2. linear OA(4¹²⁵, 256, F₄, 45) (dual of [256, 131, 46]-code), using an extension C_e(44) of the primitive narrow-sense BCH-code C(I) with length 255Â = 4⁴âˆ’1, defining interval IÂ =Â [1,44], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 45 [i]
3. linear OA(4¹¹, 25, F₄, 7) (dual of [25, 14, 8]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹¹, 26, F₄, 7) (dual of [26, 15, 8]-code), using
    - 4 times truncation [i] based on linear OA(4¹⁵, 30, F₄, 11) (dual of [30, 15, 12]-code), using
      - extended quadratic residue code Q_e(30,4) [i]

Mode: Constructive and 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(4¹⁵¹, 141, F₄, 2, 53) (dual of [(141, 2), 131, 54]-NRT-code)	[i]		OOA Folding
2	Linear OOA(4¹⁵¹, 94, F₄, 3, 53) (dual of [(94, 3), 131, 54]-NRT-code)	[i]		OOA Folding