|| Dual-containing Alternant Codes for Applications in the Calderbank–Shor–Steane Construction
||Sisi Miao, Christian Senger, University of Stuttgart, Germany|
||D5-S4-T2: Coding for Quantum Channels
||Friday, 16 July, 23:00 - 23:20
||Friday, 16 July, 23:20 - 23:40
Dual-containing classical error-correcting codes can be used in the Calderbank-Shor-Steane (CSS) construction for quantum error-correcting codes (QECCs). Dual-containing Bose-Chaudhuri-Hocquenghem (BCH) codes have been extensively studied in this regard. Research on the more general alternant codes is far less complete, despite the perspective of finding superior codes among them. In this paper, conditions for an alternant code to contain its Euclidean dual code are derived. The necessity of having dual-containing generalized Reed-Solomon (GRS) codes is shown and the structure of such codes is studied. An approach for constructing dual-containing alternant codes from BCH codes is proposed. In addition, a method for finding GRS codes over a given finite field with dual-containing alternant subfield-subcodes is presented. This method encompasses dual-containing BCH codes as a special case.