Multivariate Goppa Codes
نویسندگان
چکیده
In this paper, we introduce multivariate Goppa codes, which contain, as a particular case, the well-known classical codes. We provide parity check matrix for code in terms of tensor product generalized Reed-Solomon prove that codes are subfield subcodes augmented Cartesian By showing how new family relates to and obtain information about parameters, subcodes, duals, hulls see some instances, (resp., codes) also (resp. codes). utilize entanglement-assisted quantum error-correcting build families long LCD, self-dual, or self-orthogonal
منابع مشابه
Goppa codes
Absfruct-Goppa described a new class of linear noncyclic errorcorrecting codes in [l] and [2]. This paper is a summary of Goppa’s work, which is not yet available in English.’ We prove the four most important properties of Goppa codes. 1) There exist q-ary Goppa codes with lengths and redundancies comparable to BCH codes. For the same redundancy, the Goppa code is typically one digit longer. 2)...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2023
ISSN: ['0018-9448', '1557-9654']
DOI: https://doi.org/10.1109/tit.2022.3201692