SHI Minjia, HUANG Daitao, SOLÉ Patrick. Optimal Ternary Cubic Two-Weight Codes[J]. Chinese Journal of Electronics, 2018, 27(4): 734-738. doi: 10.1049/cje.2018.04.010
Citation: SHI Minjia, HUANG Daitao, SOLÉ Patrick. Optimal Ternary Cubic Two-Weight Codes[J]. Chinese Journal of Electronics, 2018, 27(4): 734-738. doi: 10.1049/cje.2018.04.010

Optimal Ternary Cubic Two-Weight Codes

doi: 10.1049/cje.2018.04.010
Funds:  This work is supported by National Natural Science Foundation of China (No.61672036), Excellent Youth Foundation of Natural Science Foundation of Anhui Province (No.1808085J20), Technology Foundation for Selected Overseas Chinese Scholar, Ministry of Personnel of China (No.05015133), and Key projects of support program for outstanding young talents in Colleges and Universities (No.gxyqZD2016008).
  • Received Date: 2017-07-14
  • Rev Recd Date: 2017-09-21
  • Publish Date: 2018-07-10
  • We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of a certain ring of order 27. These codes are abelian, and their ternary images are quasi-cyclic of coindex three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even. When m is odd, under some hypothesises on the size of L, we obtain two new infinite families of two-weight codes which are optimal. Applications of the image codes to secret sharing schemes are also given.
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