Additive codes over F<SUB>4</SUB>have been of great interest due to their application to quantum error correction. As another application, we introduce a new class of formally self-dual additive codes over F<SUB>4</SUB> which i...
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https://www.riss.kr/link?id=A107577830
2010
-
SCOPUS,SCIE
학술저널
787-799(13쪽)
0
상세조회0
다운로드다국어 초록 (Multilingual Abstract)
Additive codes over F<SUB>4</SUB>have been of great interest due to their application to quantum error correction. As another application, we introduce a new class of formally self-dual additive codes over F<SUB>4</SUB> which i...
Additive codes over F<SUB>4</SUB>have been of great interest due to their application to quantum error correction. As another application, we introduce a new class of formally self-dual additive codes over F<SUB>4</SUB> which is a natural analogue of the binary formally self-dual codes and is missing in the study of additive codes over F<SUB>4</SUB> In fact, Gulliver and Ostergard (2003) considered formally self-dual linear codes over F<SUB>4</SUB>of even lengths, and Choie and Sole (2008) suggested classifying formally self-dual linear codes over F<SUB>4</SUB>of odd lengths in order to study lattices from these codes. These motivate our study on formally self-dual additive codes over F<SUB>4</SUB> In this paper, we define extremal and near-extremal formally self-dual additive codes over F<SUB>4</SUB> classify all extremal codes, and construct many near-extremal codes. We discuss a general method (called the weak balance principle) for constructing such codes. We conclude with some open problems.