Search Results - "Algebraic coding theory"

The Secret of Ramsey Numbers: A new order forms out of randomness.

Authors: Edwards, Chris¹ (AUTHOR) chris@chrised.com

Source: Communications of the ACM. Jan2025, Vol. 68 Issue 1, p11-13. 3p.

Subject Terms: RAMSEY theory, ALGEBRAIC coding theory, POSTDOCTORAL researchers

People: MATTHEUS, Sam, VERSTRAETE, Jacques

New MDS and self-dual generalized Roth-Lample codes as well as their deep holes.

Authors: Li, Fengwei Jiang, Ruiyuan Liu, Yuting

Source: Designs, Codes & Cryptography; Nov2025, Vol. 93 Issue 11, p5079-5096, 18p

Subject Terms: PARITY-check matrix, ALGEBRAIC coding theory, REED-Solomon codes, CODING theory, ERROR-correcting codes

On vectorial functions mapping strict affine subspaces of their domain into strict affine subspaces of their co-domain, and the strong D-property

Authors: Carlet, Claude Piccione, Enrico

Source: Advances in Mathematics of Communications. 19:793-828

Subject Terms: affine spaces, APN, cryptography, vectorial Boolean function, permutations, Algebraic coding theory, cryptography (number-theoretic aspects), Boolean functions

File Description: application/xml

A proposed public-key cryptosystem constructed using Paley graphs

Authors: Zhour, Oumazouz

Source: International Journal of Mathematics and Computer Science. :465-468

Subject Terms: decryption algorithm, cryptographic systems, sequence of local complementations, Cryptography, Algebraic coding theory, cryptography (number-theoretic aspects), Paley graphs, encryption algorithm, quadratic residues

File Description: application/xml

Access URL: https://zbmath.org/7968952
https://doi.org/10.69793/ijmcs/02.2025/zhour

A characterization of finite commutative Frobenius rings and applications to algebraic coding theory.

Authors: Dougherty, Steven T.

Source: Advances in Mathematics of Communications; Feb2026, Vol. 20 Issue 1, p1-5, 5p

Subject Terms: ALGEBRAIC coding theory, RING theory, ALGORITHMS, IDEALS (Algebra), HYPOTHESIS, FINITE rings

New NMDS self-dual codes over finite fields.

Authors: Lebed, Khawla Zheng, Dabin Liu, Hongwei

Source: Advances in Mathematics of Communications; Feb2026, Vol. 20 Issue 1, p1-9, 9p

Subject Terms: CODING theory, FINITE fields, PARAMETERIZATION, ALGEBRAIC coding theory

Knot theory and error-correcting codes.

Authors: Kılıç, Altan B. Nijsten, Anne Pellikaan, Ruud et al.

Source: Designs, Codes & Cryptography; Aug2025, Vol. 93 Issue 8, p3029-3068, 40p

Subject Terms: KNOT theory, ERROR-correcting codes, MATHEMATICAL functions, ALGEBRAIC coding theory, CODING theory, DECODING algorithms

Well-rounded lattices from odd prime degree number fields in the ramified case.

Authors: Bastos, Jefferson Luiz Rocha de Araujo, Robson Ricardo Neto, Trajano Pires da Nóbrega et al.

Source: Advances in Geometry; Jul2025, Vol. 25 Issue 3, p361-367, 7p

Subject Terms: RINGS of integers, PRIME numbers, CODING theory, CRYPTOGRAPHY, WIRETAPPING, ALGEBRAIC coding theory

On the Terwilliger Algebra of the Group Association Scheme of the Symmetric Group Sym(7).

Authors: Herman, Allen Maleki, Roghayeh Razafimahatratra, Andriaherimanana Sarobidy

Source: Journal of Combinatorial Designs; Jul2025, Vol. 33 Issue 7, p261-274, 14p

Subject Terms: CONJUGACY classes, SYMMETRY groups, ORDERED algebraic structures, REGULAR graphs, ALGEBRAIC coding theory

On constacyclic codes of length 9ps over pm and their optimal codes.

Authors: Dinh, Hai Q. Ha, Hieu V. Nguyen, Nhan T. V. et al.

Source: Journal of Algebra & Its Applications. Jul2024, Vol. 23 Issue 8, p1-42. 42p.

Subject Terms: *HAMMING distance, *ALGEBRAIC coding theory, *PRIME numbers, *FINITE fields, *CYCLIC codes

The subfield metric and its application to quantum error correction.

Authors: Grassl, Markus Horlemann, Anna-Lena Weger, Violetta

Source: Journal of Algebra & Its Applications. Jun2024, Vol. 23 Issue 7, p1-25. 25p.

Subject Terms: *ALGEBRAIC coding theory, *FINITE fields

On the Dimensions of Hermitian Subfield Subcodes from Higher-Degree Places.

Authors: El Khalfaoui, Sabira Nagy, Gábor P.

Source: Entropy. May2024, Vol. 26 Issue 5, p386. 22p.

Subject Terms: *CODING theory, *ALGEBRAIC coding theory, *FINITE fields, *ALGEBRAIC codes, *AUTOMORPHISMS

Asymptotically optimal aperiodic quasi-complementary sequence sets based on extended Boolean functions

Authors: Shen, Bingsheng Yu, Tao Zhou, Zhengchun et al.

Source: Designs, Codes and Cryptography. 92:4213-4230

Subject Terms: Combinatorial codes, Shift register sequences and sequences over finite alphabets in information and communication theory, Cryptography, Algebraic coding theory, cryptography (number-theoretic aspects), multi-carrier code-division multiple-access, maximum aperiodic correlation magnitude, Boolean functions, extended Boolean function, quasi-complementary sequence set

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The number of self-dual cyclic codes over finite fields

Authors: Qiang Zhang

Source: Journal of Applied Mathematics and Computing. 70:5795-5803

Subject Terms: exact power character of 2, Power residues, reciprocity, Algebraic coding theory, cryptography (number-theoretic aspects), finite fields, Cyclic codes, self-dual cyclic code

File Description: application/xml

Access URL: https://zbmath.org/8036683
https://doi.org/10.1007/s12190-024-02196-z

Investigation of the permutation and linear codes from the Welch APN function

Authors: Helleseth, Tor Li, Chunlei Xia, Yongbo

Source: Designs, Codes and Cryptography
937–959

Subject Terms: algebraic decoding, cyclic codes, Decoding, Algebraic coding theory, cryptography (number-theoretic aspects), differential spectrum, permutation, Walsh spectrum, linear codes, Linear codes (general theory), Polynomials over finite fields

File Description: application/xml; application/pdf

Access URL: https://zbmath.org/8029651
https://doi.org/10.1007/s10623-024-01461-3
https://hdl.handle.net/11250/3192587

Asymptotic bounds on the numbers of certain bent functions

Authors: Potapov, Vladimir N. Özbudak, Ferruh

Source: Cryptography and Communications. 16:1289-1307

Subject Terms: bent function, Algebraic coding theory, cryptography (number-theoretic aspects), 0102 computer and information sciences, 02 engineering and technology, 01 natural sciences, Combinatorial aspects of block designs, generalized Maiorana-McFarland bent function, transversal, Cryptography, 0202 electrical engineering, electronic engineering, information engineering, Orthogonal arrays, Latin squares, Room squares, Boolean functions, subspace design

File Description: application/xml

Access URL: https://zbmath.org/7985183
https://doi.org/10.1007/s12095-024-00726-x

CRT representation of LWE Based TFHE: CRT representation of LWE based TFHE

Authors: Mehmet Özen Serra Sazoğlu Ünal Çavuşoğlu et al.

Source: Computational and Applied Mathematics. 44

Subject Terms: homomorphic encryption, Algebraic coding theory, cryptography (number-theoretic aspects), Chinese remainder theorem (CRT), torus fully homomorphic encryption (TFHE)

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Meet-in-the-middle attack on round-reduced SCARF under single pair-of-tweaks setting.

Authors: Chen, Siwei Hu, Kai Liu, Guozhen et al.

Source: Designs, Codes & Cryptography; May2025, Vol. 93 Issue 5, p1531-1547, 17p

Subject Terms: ALGEBRAIC coding theory, TIME complexity, BLOCK ciphers, LINEAR equations, LINEAR systems, BLOCK designs

On Algebraic Properties of Primitive Eisenstein Integers with Applications in Coding Theory.

Authors: Hadi, Abdul Isnaini, Uha Wijayanti, Indah Emilia et al.

Source: Entropy; Apr2025, Vol. 27 Issue 4, p337, 23p

Subject Terms: PRIME numbers, QUOTIENT rings, CYCLIC groups, CODING theory, RINGS of integers, ALGEBRAIC coding theory

Bent functions satisfying the dual bent condition and permutations with the $$(\mathcal {A}_m)$$ property: Bent functions satisfying the dual bent condition and permutations with the \((\mathcal{A}_m)\) property

Authors: Alexandr Polujan Enes Pasalic Sadmir Kudin et al.

Source: Cryptography and Communications. 16:1235-1256

Subject Terms: FOS: Computer and information sciences, Boolean bent function, Maiorana-McFarland class, Computer Science - Information Theory, Information Theory (cs.IT), bent 4-concatenation, equivalence, FOS: Mathematics, Algebraic coding theory, cryptography (number-theoretic aspects), Mathematics - Combinatorics, Combinatorics (math.CO), Boolean functions, dual bent condition

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Access URL: http://arxiv.org/abs/2310.10162
https://zbmath.org/7985181
https://doi.org/10.1007/s12095-024-00724-z