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CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES

Year 2014, Volume: 63 Issue: 2, 147 - 161, 01.08.2014

Abdullah Paşa Bahattin Yıldız

https://doi.org/10.1501/Commua1_0000000720

Keywords

Projective geometries Hyperplanes Gray Map Homogeneous weight Finite chain rings Rk

References

  • E.F. Assmus, J.D. Key, Polynomial codes and …nite geometries, in V.S. Pless, W.C. Hufman Handbook of Coding Theory, 2-2 (1998), 1269-1343.
  • C. Bachoc, Applications of coding theory to the construction of modular lattices, J. Comb. Theory, Ser. A, 78 (1997), 92-119.
  • A. Bonnecaze, P. Udaya, Cyclic codes and self-dual codes over F2+ uF2, IEEE Trans. Inf. Theory 45 (1998), 1250-1255.
  • C. Carlet, Z2k-linear Codes, IEEE Trans. Inf. Theory 44 (1998), 1543-1547.
  • I. Constantinescu, W. Heise, A metric for codes over residue class rings of integers, Probl. Peredachi Inf. 33 (1997), 22-26.
  • S.T. Dougherty, M. Harada, P. Gaborit, P. Solé, Type II codes over F+ uF2, IEEE Trans. Inf. Theory 45 (1999), 32-45.
  • S.T. Dougherty, B. Yildiz, S. Karadeniz, Codes over Rk, Gray maps and their binary images, Finite Fields Appl. 17 (2011), 205-219.
  • M. Greferath, S.E. Schmidt, Gray isometries for …nite chain rings and a nonlinear ternary (36; 3; 15) code, IEEE Trans. Inf. Theory 45 (1999), 2522-2524.
  • A.R. Hammons, V. Kumar, A.R. Calderbank, N.J.A. Sloane, P. Solé, The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inf. Theory 40 (1999), 301
  • T. Honold, I. Landjev, Linear codes over …nite chain rings, Electron. J. Comb. 7 (1998), 126.
  • W.C. Huğman, Decompositions and extremal Type II codes over Z4, IEEE Trans. Inf. Theory (1998) 800-809.
  • P. Solé, S. Ling, Duadic codes over F2+ uF, Appl. Algebra Eng. Commun. Comput. 12 (2001), 365-379.
  • J. Wood, Duality for modules over nite rings and application to coding theory, Am. J. Math. (1999), 551-575.
  • B. Yildiz, Weight enumerators and Gray maps of linear codes over rings, Ph.D. Thesis, California Institute of Technology, 2006.
  • B. Yildiz, A Combinatorial construction of the Gray map over Galois rings, Discrete Math. (2009), 3408-3412.
  • B. Yildiz, S. Karadeniz, Linear Codes over F2+ uF2+ vF+ uvF, Des. Codes Cryptography (2010), 61-81.
  • B. Yildiz, S. Karadeniz, Self Dual Codes over F2+ uF2+ vF2+ uvF2, J. Franklin Inst. 347 (2010), 1888-1894.
  • B. Yildiz, S. Karadeniz, Cyclic Codes over F+ uF2+ vF+ uvF, Des. Codes Cryptography (2011), 221-234.
  • B. Yildiz, S. Karadeniz, Double circulant and bordered-double circulant constructions for self-dual codes over F2+ uF2+ vF2+ uvF2, Adv. Math. Commun. 6 (2012), 193–202.

Year 2014, Volume: 63 Issue: 2, 147 - 161, 01.08.2014

Abdullah Paşa Bahattin Yıldız

https://doi.org/10.1501/Commua1_0000000720

References

  • E.F. Assmus, J.D. Key, Polynomial codes and …nite geometries, in V.S. Pless, W.C. Hufman Handbook of Coding Theory, 2-2 (1998), 1269-1343.
  • C. Bachoc, Applications of coding theory to the construction of modular lattices, J. Comb. Theory, Ser. A, 78 (1997), 92-119.
  • A. Bonnecaze, P. Udaya, Cyclic codes and self-dual codes over F2+ uF2, IEEE Trans. Inf. Theory 45 (1998), 1250-1255.
  • C. Carlet, Z2k-linear Codes, IEEE Trans. Inf. Theory 44 (1998), 1543-1547.
  • I. Constantinescu, W. Heise, A metric for codes over residue class rings of integers, Probl. Peredachi Inf. 33 (1997), 22-26.
  • S.T. Dougherty, M. Harada, P. Gaborit, P. Solé, Type II codes over F+ uF2, IEEE Trans. Inf. Theory 45 (1999), 32-45.
  • S.T. Dougherty, B. Yildiz, S. Karadeniz, Codes over Rk, Gray maps and their binary images, Finite Fields Appl. 17 (2011), 205-219.
  • M. Greferath, S.E. Schmidt, Gray isometries for …nite chain rings and a nonlinear ternary (36; 3; 15) code, IEEE Trans. Inf. Theory 45 (1999), 2522-2524.
  • A.R. Hammons, V. Kumar, A.R. Calderbank, N.J.A. Sloane, P. Solé, The Z4-linearity of Kerdock, Preparata, Goethals and related codes, IEEE Trans. Inf. Theory 40 (1999), 301
  • T. Honold, I. Landjev, Linear codes over …nite chain rings, Electron. J. Comb. 7 (1998), 126.
  • W.C. Huğman, Decompositions and extremal Type II codes over Z4, IEEE Trans. Inf. Theory (1998) 800-809.
  • P. Solé, S. Ling, Duadic codes over F2+ uF, Appl. Algebra Eng. Commun. Comput. 12 (2001), 365-379.
  • J. Wood, Duality for modules over nite rings and application to coding theory, Am. J. Math. (1999), 551-575.
  • B. Yildiz, Weight enumerators and Gray maps of linear codes over rings, Ph.D. Thesis, California Institute of Technology, 2006.
  • B. Yildiz, A Combinatorial construction of the Gray map over Galois rings, Discrete Math. (2009), 3408-3412.
  • B. Yildiz, S. Karadeniz, Linear Codes over F2+ uF2+ vF+ uvF, Des. Codes Cryptography (2010), 61-81.
  • B. Yildiz, S. Karadeniz, Self Dual Codes over F2+ uF2+ vF2+ uvF2, J. Franklin Inst. 347 (2010), 1888-1894.
  • B. Yildiz, S. Karadeniz, Cyclic Codes over F+ uF2+ vF+ uvF, Des. Codes Cryptography (2011), 221-234.
  • B. Yildiz, S. Karadeniz, Double circulant and bordered-double circulant constructions for self-dual codes over F2+ uF2+ vF2+ uvF2, Adv. Math. Commun. 6 (2012), 193–202.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Articles
Authors

Abdullah Paşa This is me

Bahattin Yıldız This is me

Publication Date August 1, 2014
Published in Issue Year 2014 Volume: 63 Issue: 2

Cite

APA Paşa, A., & Yıldız, B. (2014). CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 63(2), 147-161. https://doi.org/10.1501/Commua1_0000000720
AMA Paşa A, Yıldız B. CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. August 2014;63(2):147-161. doi:10.1501/Commua1_0000000720
Chicago Paşa, Abdullah, and Bahattin Yıldız. “CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63, no. 2 (August 2014): 147-61. https://doi.org/10.1501/Commua1_0000000720.
EndNote Paşa A, Yıldız B (August 1, 2014) CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63 2 147–161.
IEEE A. Paşa and B. Yıldız, “CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 63, no. 2, pp. 147–161, 2014, doi: 10.1501/Commua1_0000000720.
ISNAD Paşa, Abdullah - Yıldız, Bahattin. “CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 63/2 (August 2014), 147-161. https://doi.org/10.1501/Commua1_0000000720.
JAMA Paşa A, Yıldız B. CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63:147–161.
MLA Paşa, Abdullah and Bahattin Yıldız. “CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 63, no. 2, 2014, pp. 147-61, doi:10.1501/Commua1_0000000720.
Vancouver Paşa A, Yıldız B. CONSTRUCTING GRAY MAPS FROM COMBINATORIAL GEOMETRIES. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2014;63(2):147-61.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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