MinT - Information on Result #677154

Information on Result #677154

Linear OA(3²⁴⁷, 263, F₃, 146) (dual of [263, 16, 147]-code), using constructionÂ X applied to C_e(151) âŠ‚ C_e(133) based on

linear OA(3²³², 243, F₃, 152) (dual of [243, 11, 153]-code), using an extension C_e(151) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,151], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 152 [i]
linear OA(3²²⁷, 243, F₃, 134) (dual of [243, 16, 135]-code), using an extension C_e(133) of the primitive narrow-sense BCH-code C(I) with length 242Â = 3⁵âˆ’1, defining interval IÂ =Â [1,133], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 134 [i]
linear OA(3¹⁵, 20, F₃, 11) (dual of [20, 5, 12]-code), using
- residual code [i] based on linear OA(3⁵⁰, 56, F₃, 35) (dual of [56, 6, 36]-code), using
  - dual code (with bound on d by constructionÂ Y1) [i] based on
    1. linear OA(3⁶, 56, F₃, 3) (dual of [56, 50, 4]-code or 56-cap in PG(5,3)), using
      - the Hill cap [i]
    2. nonexistence of linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), because
      - 20 is the largest size of a cap in PG(4,Â 3) [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OA(3²⁴⁷, 263, F₃, 145) (dual of [263, 16, 146]-code)	[i]	Strength Reduction
2	Linear OA(3²⁴⁷, 263, F₃, 144) (dual of [263, 16, 145]-code)	[i]	Strength Reduction
3	Linear OA(3²⁴⁸, 264, F₃, 146) (dual of [264, 16, 147]-code)	[i]	Code Embedding in Larger Space
4	Linear OA(3²⁴⁶, 262, F₃, 145) (dual of [262, 16, 146]-code)	[i]	Truncation
5	Linear OA(3²⁴⁵, 261, F₃, 144) (dual of [261, 16, 145]-code)	[i]
6	Linear OA(3²⁴⁴, 260, F₃, 143) (dual of [260, 16, 144]-code)	[i]
7	Linear OA(3²⁴², 258, F₃, 141) (dual of [258, 16, 142]-code)	[i]
8	Linear OOA(3²⁴⁷, 131, F₃, 2, 146) (dual of [(131, 2), 15, 147]-NRT-code)	[i]	OOA Folding
9	Linear OOA(3²⁴⁷, 87, F₃, 3, 146) (dual of [(87, 3), 14, 147]-NRT-code)	[i]	OOA Folding