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Title of Journal: Des Codes Cryptogr

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Abbravation: Designs, Codes and Cryptography

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Springer US

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DOI

10.1016/0304-5102(94)87003-9

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1573-7586

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Some cyclic codes of length 2Emphasis Type="Itali

Authors: Sudhir Batra S K Arora
Publish Date: 2010/10/09
Volume: 61, Issue: 1, Pages: 41-69
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Abstract

Explicit expressions for 4n + 2 primitive idempotents in the semisimple group ring R 2pnequiv fracGFqxx2pn1 are obtained where p and q are distinct odd primes n ≥ 1 is an integer and q has order fracphi2pn2 modulo 2p n The generator polynomials the dimension the minimum distance of the minimal cyclic codes of length 2p n generated by these 4n + 2 primitive idempotents are discussed For n = 1 the properties of some 2p p cyclic codes containing the above minimal cyclic codes are analyzed in particular The minimum weight of some subset of each of these 2p p codes are observed to satisfy a square root bound

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Other Papers In This Journal:
  1. Composition of recursions and nonlinear complexity of periodic binary sequences
  2. Practical-time attacks against reduced variants of MISTY1
  3. On the largest affine sub-families of a family of NFSR sequences
  4. The dimension of subcode-subfields of shortened generalized Reed–Solomon codes
  5. On explicit factors of cyclotomic polynomials over finite fields
  6. Two classes of optimal two-dimensional OOCs
  7. Sequences with small correlation
  8. Improved algorithms for finding low-weight polynomial multiples in $$\mathbb {F}_{2}^{}[x]$$ and some cryptographic applications
  9. A tight asymptotic bound on the size of constant-weight conflict-avoiding codes
  10. Distinguisher-based attacks on public-key cryptosystems using Reed–Solomon codes
  11. A new table of permutation codes
  12. Bent functions embedded into the recursive framework of $${\mathbb{Z}}$$ -bent functions
  13. Nonexistence of CW (110, 100)
  14. Point compression for the trace zero subgroup over a small degree extension field
  15. The Diffie–Hellman problem and generalization of Verheul’s theorem
  16. Modular independence and generator matrices for codes over $${\mathbb {Z}_m}$$
  17. Improved lower bounds on sizes of single-error correcting codes
  18. A combinatorial problem related to sparse systems of equations
  19. Some results concerning cryptographically significant mappings over GF(2 n )
  20. A note on the reducibility of binary affine polynomials
  21. Primitive normal bases for quartic and cubic extensions: a geometric approach
  22. Computing isogenies between supersingular elliptic curves over $${\mathbb {F}}_p$$
  23. On the correlation distribution of Delsarte–Goethals sequences
  24. Algebraic decoding of folded Gabidulin codes
  25. Inner balance of symmetric designs
  26. On the construction of Griesmer codes of dimension 5
  27. Applications of representation theory to wireless communications
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