Results 11 to 20 of about 563,145 (166)
Algorithms for Majority Decoding of Group Codes
Моделирование и анализ информационных систем, 2015 We consider a problem of constructive description and justification of the algorithms necessary for a practical implementation of the majority decoder for group codes specified as left ideals of groupalgebras.
V. M. Deundyak, Y. V. Kosolapov
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Extended binary Golay codes by a group algebra of one group
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2020 Extended binary Golay codes are examples of extreme binary self-dual codes of Type II (linear binary self-dual codes with Hamming distance between arbitrary codewords which are multiples of 4 that has the highest possible minimum Hamming distance among ...
М. Ю. Бортош +1 more
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Cryptosystem Based on Induced Group Codes
Моделирование и анализ информационных систем, 2016 The code C on a group G, induced by the code N on a subgroup H, has the property that for decoding the code C one can use the decoder for the code N.
V. M. Deundyak, Y. V. Kosolapov
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Block-coded modulation using two-level group codes over generalized quaternion groups [PDF]
IEEE Transactions on Information Theory, 1999 Summary: A length \(n\) group code over a group \(G\) is a subgroup of \(G^n\) under component-wise group operation. Two-level group codes over the class of generalized quaternion groups, \(Q_{2^m}\), \(m\geq 3\), are constructed using a binary code and a code over \(Z_{2^{m-1}}\), the ring of integers modulo \(2^{m-1}\), as component codes and a ...
Selvakumaran, TV, Rajan, Sundar B
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Sultan Qaboos University Journal for Science, 2009 The group of characters of an elementary Abelian group has been used to define duality between its subgroups, which in turn is extended to duality between group codes.
Adnan Abdulla Zain
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New Two-Stage Automorphism Group Decoders for Cyclic Codes
IEEE Access, 2020 Recently, error correcting codes in the erasure channel have drawn great attention for various applications such as distributed storage systems and wireless sensor networks, but many of their decoding algorithms are not practical because they have higher
Chanki Kim, Jong-Seon No
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Codes in Dihedral Group Algebra
Моделирование и анализ информационных систем, 2018 Robert McEliece developed an asymmetric encryption algorithm based on the use of binary Goppa codes in 1978 and no effective key attacks has been described yet.
Kirill V. Vedenev, Vladimir M. Deundyak
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IEEE Transactions on Information Theory, 2000 Summary: We construct a class of codes of length \(n\) such that the minimum distance \(d\) outside of a certain subcode is, up to a constant factor, bounded below by the square root of \(n\), a well-known property of quadratic residue codes. The construction, using the group algebra of an abelian group and a special partition or splitting of the group,
Ding, C., Kohel, D.R., Ling, S.
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LCD codes and LCP of codes from units of group rings
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 A linear code with complementary dual(LCD) is a linear code such that LCD codes are of greatimportance due to their wide range of applications in consumer electronics,storage systems and cryptography. Group rings have a rich source of units. Alsothe well-
Mehmet Emin Köroğlu
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On a relation between GAG codes and AG codes
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code.
Şenel Engin, Öke Figen
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