-
Previous Article
On Abelian group representability of finite groups
- AMC Home
- This Issue
-
Next Article
Nearest-neighbor entropy estimators with weak metrics
On the covering radius of some modular codes
1. | Laboratory of Natural Information Processing, Dhirubhai Ambani Institute of Information and Communication Technology, Gandhinagar, Gujarat 382007, India |
2. | Department of Mathematics, School of Mathematical Sciences, Bharathidasan University, Tiruchirappalli, Tamil Nadu 620024, India |
References:
[1] |
T. Aoki, P. Gaborit, M. Harada, M. Ozeki and P. Solé, On the covering radius of $\mathbb Z_{4}$ codes and their lattices, IEEE Trans. Inform. Theory, 45 (1999), 2162-2168.
doi: 10.1109/18.782168. |
[2] |
E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II codes, even unimodular lattices and invariant rings, IEEE Trans. Inform. Theory, 45 (1999), 1194-1205.
doi: 10.1109/18.761269. |
[3] |
M. C. Bhandari, M. K. Gupta and A. K. Lal, On $\mathbb Z_4$ simplex codes and their gray images, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, 1999, 170-179.
doi: 10.1007/3-540-46796-3_17. |
[4] |
A. Bonnecaze, P. Solé, C. Bachoc and B. Mourrain, Type II codes over $\mathbb Z_4$, IEEE Trans. Inform. Theory, 43 (1997), 969-976.
doi: 10.1109/18.568705. |
[5] |
A. Bonnecaze, P. Solé and A. R. Calderbank, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory, 41 (1995), 366-377.
doi: 10.1109/18.370138. |
[6] |
C. Carlet, $\mathbb Z_{2^k}$-linear codes, IEEE Trans. Inform. Theory, 44 (1998), 1543-1547.
doi: 10.1109/18.681328. |
[7] |
C. Cohen, I. Honkala, S. Litsyn and A. Lobstein, Covering Codes, Elsevier, 1997. |
[8] |
G. D. Cohen, M. G. Karpovsky, H. F. Mattson and J. R. Schatz, Covering radius-survey and recent results, IEEE Trans. Inform. Theory, 31 (1985), 328-343.
doi: 10.1109/TIT.1985.1057043. |
[9] |
C. J. Colbourn and M. K. Gupta, On quaternary MacDonald codes, in Proc. Information Technology: Coding and Computing, 2003, 212-215.
doi: 10.1109/ITCC.2003.1197528. |
[10] |
I. Constantinescu, W. Heise and T. Honold, Monomial extensions of isometries between codes over $\mathbb Z_m$, in Proc. Workshop ACCT'96, Sozopol, Bulgaria, 1996, 98-104. |
[11] |
J. H. Conway and N. J. A. Sloane, Self-dual codes over the integers modulo $4$, J. Combin. Theory Ser. A, 62 (1993), 30-45.
doi: 10.1016/0097-3165(93)90070-O. |
[12] |
S. Dodunekov and J. Simonis, Codes and projective multisets, Electr. J. Combin., 5 (1998), R37. |
[13] |
S. T. Dougherty, T. A. Gulliver and M. Harada, Type II codes over finite rings and even unimodular lattices, J. Alg. Combin., 9 (1999), 233-250.
doi: 10.1023/A:1018696102510. |
[14] |
S. T. Dougherty, M. Harada and P. Solé, Self-dual codes over rings and the Chinese remainder theorem, Hokkaido Math. J., 28 (1999), 253-283.
doi: 10.14492/hokmj/1351001213. |
[15] |
S. T. Dougherty, M. Harada and P. Solé, Shadow codes over $\mathbb Z_4$, Finite Fields Appl., 7 (2001), 507-529.
doi: 10.1006/ffta.2000.0312. |
[16] |
C. Durairajan, On Covering Codes and Covering Radius of Some Optimal Codes, Ph.D Thesis, Department of Mathematics, IIT Kanpur, 1996. |
[17] |
T. A. Gulliver and M. Harada, Double circulant self dual codes over $\mathbb Z_{2k}$, IEEE Trans. Inform. Theory, 44 (1998), 3105-3123.
doi: 10.1109/18.737540. |
[18] |
A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, A linear construction for certain Kerdock and Preparata codes, Bull Amer. Math. Soc., 29 (1993), 218-222.
doi: 10.1090/S0273-0979-1993-00426-9. |
[19] |
A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $\mathbb Z_4$-linearity of kerdock, preparata, goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[20] |
M. Harada, New extremal Type II codes over $\mathbb Z_4$, Des. Codes Cryptogr., 13 (1998), 271-284.
doi: 10.1023/A:1008254008212. |
[21] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in The Handbook of Coding Theory (eds. V. Pless and W.C. Huffman), North-Holland, 1998. |
[22] |
V. V. Vazirani, H. Saran and B. SundarRajan, An efficient algorithm for constructing minimal trellises for codes over finite abelian groups, IEEE Trans. Inform. Theory, 42 (1996), 1839-1854.
doi: 10.1109/18.556679. |
show all references
References:
[1] |
T. Aoki, P. Gaborit, M. Harada, M. Ozeki and P. Solé, On the covering radius of $\mathbb Z_{4}$ codes and their lattices, IEEE Trans. Inform. Theory, 45 (1999), 2162-2168.
doi: 10.1109/18.782168. |
[2] |
E. Bannai, S. T. Dougherty, M. Harada and M. Oura, Type II codes, even unimodular lattices and invariant rings, IEEE Trans. Inform. Theory, 45 (1999), 1194-1205.
doi: 10.1109/18.761269. |
[3] |
M. C. Bhandari, M. K. Gupta and A. K. Lal, On $\mathbb Z_4$ simplex codes and their gray images, in Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, Springer, 1999, 170-179.
doi: 10.1007/3-540-46796-3_17. |
[4] |
A. Bonnecaze, P. Solé, C. Bachoc and B. Mourrain, Type II codes over $\mathbb Z_4$, IEEE Trans. Inform. Theory, 43 (1997), 969-976.
doi: 10.1109/18.568705. |
[5] |
A. Bonnecaze, P. Solé and A. R. Calderbank, Quaternary quadratic residue codes and unimodular lattices, IEEE Trans. Inform. Theory, 41 (1995), 366-377.
doi: 10.1109/18.370138. |
[6] |
C. Carlet, $\mathbb Z_{2^k}$-linear codes, IEEE Trans. Inform. Theory, 44 (1998), 1543-1547.
doi: 10.1109/18.681328. |
[7] |
C. Cohen, I. Honkala, S. Litsyn and A. Lobstein, Covering Codes, Elsevier, 1997. |
[8] |
G. D. Cohen, M. G. Karpovsky, H. F. Mattson and J. R. Schatz, Covering radius-survey and recent results, IEEE Trans. Inform. Theory, 31 (1985), 328-343.
doi: 10.1109/TIT.1985.1057043. |
[9] |
C. J. Colbourn and M. K. Gupta, On quaternary MacDonald codes, in Proc. Information Technology: Coding and Computing, 2003, 212-215.
doi: 10.1109/ITCC.2003.1197528. |
[10] |
I. Constantinescu, W. Heise and T. Honold, Monomial extensions of isometries between codes over $\mathbb Z_m$, in Proc. Workshop ACCT'96, Sozopol, Bulgaria, 1996, 98-104. |
[11] |
J. H. Conway and N. J. A. Sloane, Self-dual codes over the integers modulo $4$, J. Combin. Theory Ser. A, 62 (1993), 30-45.
doi: 10.1016/0097-3165(93)90070-O. |
[12] |
S. Dodunekov and J. Simonis, Codes and projective multisets, Electr. J. Combin., 5 (1998), R37. |
[13] |
S. T. Dougherty, T. A. Gulliver and M. Harada, Type II codes over finite rings and even unimodular lattices, J. Alg. Combin., 9 (1999), 233-250.
doi: 10.1023/A:1018696102510. |
[14] |
S. T. Dougherty, M. Harada and P. Solé, Self-dual codes over rings and the Chinese remainder theorem, Hokkaido Math. J., 28 (1999), 253-283.
doi: 10.14492/hokmj/1351001213. |
[15] |
S. T. Dougherty, M. Harada and P. Solé, Shadow codes over $\mathbb Z_4$, Finite Fields Appl., 7 (2001), 507-529.
doi: 10.1006/ffta.2000.0312. |
[16] |
C. Durairajan, On Covering Codes and Covering Radius of Some Optimal Codes, Ph.D Thesis, Department of Mathematics, IIT Kanpur, 1996. |
[17] |
T. A. Gulliver and M. Harada, Double circulant self dual codes over $\mathbb Z_{2k}$, IEEE Trans. Inform. Theory, 44 (1998), 3105-3123.
doi: 10.1109/18.737540. |
[18] |
A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, A linear construction for certain Kerdock and Preparata codes, Bull Amer. Math. Soc., 29 (1993), 218-222.
doi: 10.1090/S0273-0979-1993-00426-9. |
[19] |
A. R. Hammons, P. V. Kumar, A. R. Calderbank, N. J. A. Sloane and P. Solé, The $\mathbb Z_4$-linearity of kerdock, preparata, goethals, and related codes, IEEE Trans. Inform. Theory, 40 (1994), 301-319.
doi: 10.1109/18.312154. |
[20] |
M. Harada, New extremal Type II codes over $\mathbb Z_4$, Des. Codes Cryptogr., 13 (1998), 271-284.
doi: 10.1023/A:1008254008212. |
[21] |
E. M. Rains and N. J. A. Sloane, Self-dual codes, in The Handbook of Coding Theory (eds. V. Pless and W.C. Huffman), North-Holland, 1998. |
[22] |
V. V. Vazirani, H. Saran and B. SundarRajan, An efficient algorithm for constructing minimal trellises for codes over finite abelian groups, IEEE Trans. Inform. Theory, 42 (1996), 1839-1854.
doi: 10.1109/18.556679. |
[1] |
Sergio R. López-Permouth, Steve Szabo. On the Hamming weight of repeated root cyclic and negacyclic codes over Galois rings. Advances in Mathematics of Communications, 2009, 3 (4) : 409-420. doi: 10.3934/amc.2009.3.409 |
[2] |
Rafael Arce-Nazario, Francis N. Castro, Jose Ortiz-Ubarri. On the covering radius of some binary cyclic codes. Advances in Mathematics of Communications, 2017, 11 (2) : 329-338. doi: 10.3934/amc.2017025 |
[3] |
Nabil Bennenni, Kenza Guenda, Sihem Mesnager. DNA cyclic codes over rings. Advances in Mathematics of Communications, 2017, 11 (1) : 83-98. doi: 10.3934/amc.2017004 |
[4] |
Zihui Liu. Galois LCD codes over rings. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022002 |
[5] |
Tsonka Baicheva, Iliya Bouyukliev. On the least covering radius of binary linear codes of dimension 6. Advances in Mathematics of Communications, 2010, 4 (3) : 399-404. doi: 10.3934/amc.2010.4.399 |
[6] |
Aicha Batoul, Kenza Guenda, T. Aaron Gulliver. Some constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2016, 10 (4) : 683-694. doi: 10.3934/amc.2016034 |
[7] |
Somphong Jitman, San Ling, Patanee Udomkavanich. Skew constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2012, 6 (1) : 39-63. doi: 10.3934/amc.2012.6.39 |
[8] |
Kanat Abdukhalikov. On codes over rings invariant under affine groups. Advances in Mathematics of Communications, 2013, 7 (3) : 253-265. doi: 10.3934/amc.2013.7.253 |
[9] |
Delphine Boucher, Patrick Solé, Felix Ulmer. Skew constacyclic codes over Galois rings. Advances in Mathematics of Communications, 2008, 2 (3) : 273-292. doi: 10.3934/amc.2008.2.273 |
[10] |
Eimear Byrne. On the weight distribution of codes over finite rings. Advances in Mathematics of Communications, 2011, 5 (2) : 395-406. doi: 10.3934/amc.2011.5.395 |
[11] |
Steven T. Dougherty, Esengül Saltürk, Steve Szabo. Codes over local rings of order 16 and binary codes. Advances in Mathematics of Communications, 2016, 10 (2) : 379-391. doi: 10.3934/amc.2016012 |
[12] |
Gianira N. Alfarano, Anina Gruica, Julia Lieb, Joachim Rosenthal. Convolutional codes over finite chain rings, MDP codes and their characterization. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022028 |
[13] |
Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Addendum. Advances in Mathematics of Communications, 2011, 5 (3) : 543-546. doi: 10.3934/amc.2011.5.543 |
[14] |
Alonso sepúlveda Castellanos. Generalized Hamming weights of codes over the $\mathcal{GH}$ curve. Advances in Mathematics of Communications, 2017, 11 (1) : 115-122. doi: 10.3934/amc.2017006 |
[15] |
Joaquim Borges, Josep Rifà, Victor Zinoviev. Completely regular codes by concatenating Hamming codes. Advances in Mathematics of Communications, 2018, 12 (2) : 337-349. doi: 10.3934/amc.2018021 |
[16] |
Washiela Fish, Jennifer D. Key, Eric Mwambene. Partial permutation decoding for simplex codes. Advances in Mathematics of Communications, 2012, 6 (4) : 505-516. doi: 10.3934/amc.2012.6.505 |
[17] |
Nupur Patanker, Sanjay Kumar Singh. Generalized Hamming weights of toric codes over hypersimplices and squarefree affine evaluation codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021013 |
[18] |
Thomas Westerbäck. Parity check systems of nonlinear codes over finite commutative Frobenius rings. Advances in Mathematics of Communications, 2017, 11 (3) : 409-427. doi: 10.3934/amc.2017035 |
[19] |
Zihui Liu, Dajian Liao. Higher weights and near-MDR codes over chain rings. Advances in Mathematics of Communications, 2018, 12 (4) : 761-772. doi: 10.3934/amc.2018045 |
[20] |
Steven T. Dougherty, Abidin Kaya, Esengül Saltürk. Cyclic codes over local Frobenius rings of order 16. Advances in Mathematics of Communications, 2017, 11 (1) : 99-114. doi: 10.3934/amc.2017005 |
2020 Impact Factor: 0.935
Tools
Metrics
Other articles
by authors
[Back to Top]