Updates in reverse chronological order

Below we provide information on new entries, starting on 2020-07-17.

Linear Block Codes

GF(2)

2022-08-11
quasicylic codes [234,51,63]2 and [234,52,62]2 by
Fernando Hernando, Francisco D. Igual, and Gregorio Quintana-Ortí,
"Algorithm 994: Fast Implementations of the Brouwer-Zimmermann Algorithm for the Computation of the Minimum Distance of a Random Linear Code,"
ACM Transactions on Mathematical Software, 45(2), article no. 23, June 2019,
DOI 10.1145/3302389
5 derived codes
2021-08-31
codes via puncturing shortened cyclic codes:
[113,28,33]2, [216,42,63]2, [220,42,65]2,
7 derived codes
2021-08-19
quasicyclic code [111,38,25]2 by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey arXiv:2108.10316,
1 derived code
2021-08-12
codes [99,31,26]2 and [178,52,42]2 by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey arXiv:2108.06752 via Construction X using quasicyclic codes,
6 derived codes
2021-08-12
code [119,30,34]2 by Eric Chen, applying Construction X to quasicyclic codes [116,30,32]2 and [116,28,34]2,
1 derived code
2021-04-23
codes via puncturing cyclic and shortened cyclic codes:
[213,30,73]2, [227,36,73]2, [229,35,75]2, [230,33,77]2 from
Motoyuki Watanabe and Masakatu Morii,
"A New Method for Constructing Good Linear Codes; updating on the minimum distance of some linear codes,"
Proc. SITA2012, pp.636-638, Dec. 2012.
[216,30,75]2, [220,47,61]2, [224,34,73]2, [224,42,67]2, [224,47,63]2, [225,40,69]2, [228,42,69]2, [228,45,67]2, [229,47,66]2, [230,41,71]2, [231,39,73]2, [231,47,67]2, [232,37,75]2, [232,45,69]2, [234,44,71]2, [235,42,73]2, [235,47,69]2, [237,45,72]2, [238,47,71]2, [239,45,73]2, [241,47,73]2, [242,45,75]2 from
Takuya Ohara, Makoto Takita and Masakatu Morii,
"A Construction of Binary Punctured Linear Codes and A Supporting Method for Best Code Search,"
Proc. 2020 International Symposium on Information Theory and Its Applications (ISITA), Oct. 2020.
IEEE Xplore: 9366122
173 derived codes
2020-10-14
puncturing [240,21,104]2 at specific positions:
[208,21,81]2, [210,21,82]2, [213,21,84]2, [215,21,85]2, [218,21,87]2, [220,21,88]2, [223,21,90]2, [226,21,92]2, [229,21,94]2,
24 derived codes
2020-10-14
applying Construction X to Goppa codes of length 240:
[254,22,106]2, [249,21,106]2,
6 derived codes
2020-10-14
Goppa code [240,21,104]2, contributed by Jan L. Carrasquillo López, Axel O. Gómez Flores, Fernando Piñero, and Christopher Soto
28 derived codes
Jan L. Carrasquillo-López, Axel O. Gómez-Flores, Christopher Soto, Fernando Piñero,
"Introducing Three Best Known Goppa Codes,"
arXiv:2010.07278 [cs.IT], October 2020

GF(3)

2021-09-18
quasicyclic code [176,43,61]3,
34 derived codes
2021-08-29
code [102,27,37]3 via Construction X applied to quasicyclic code [99,27,35]3 and quasicyclic code [99,25,37]3
2021-08-27
code [124,28,48]3 via Construction X applied to quasicyclic code [112,28,42]3 and quasicyclic code [112,22,48]3,
3 derived codes
2021-08-26
the following codes are obtained applying Construction XX to quasicylic codes:
[106,23,43]3, [109,23,44]3, [142,26,60]3, [167,23,77]3, [169,23,78]3, [171,27,74]3, [175,26,77]3, [177,26,78]3,
4 derived codes
2021-08-26
code [179,40,64]3 via Construction X applied to quasicyclic code [176,40,62]3 and quasicyclic code [176,38,64]3,
3 derived codes
2021-08-25
code [177,18,90]3 via Construction X applied to quasicyclic code [176,18,89]3 and quasicyclic code [176,17,90]3
2021-08-25
quasicyclic code [176,18,89]3,
1 derived code
2021-08-25
quasicyclic code [176,40,62]3,
2 derived codes
2021-08-19
quasicyclic code [176,39,64]3,
11 derived codes
2021-08-18
code [178,38,66]3 applying Construction X to quasicyclic codes [176,38,64]3 and [176,37,66]3,
1 derived code
2021-08-17
quasicyclic code [176,37,66]3,
4 derived codes
2021-08-13
the following codes are obtained by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey arXiv:2108.06752 applying Construction X to quasicylic codes:
[100,28,35]3, [101,26,37]3, [107,23,43]3, [108,31,36]3, [114,23,48]3, [190,24,88]3, [161,27,69]3, [164,27,70]3, [167,27,72]3, [170,26,75]3, [170,27,73]3, [219,14,123]3,
12 derived cdoes
2021-08-13
quasicyclic code [112,23,46]3 by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey arXiv:2108.06752
2021-08-12
code [178,18,90]3 by Eric Chen, applying Construction X to quasicyclic codes [176,18,88]3 and [176,17,90]3,
1 derived code

GF(4)

2022-11-10-29
constacyclic code [111,90,9]4 contributed by Dastbasteh & Lisonek arXiv 2211.00897
and supercode [111,91,9]4
38 derived codes
2020-09-29
quasicyclic code [88,45,21]4 from a skew-cyclic code, contributed by Padmapani Seneviratne
1 derived code
2020-09-23
code [109,63,28]4
via Construction X from constacyclic codes
9 derived codes
2020-08-31
constacyclic code [105,63,18]4
12 derived codes
2020-08-23
quasicyclic code from a skew-cyclic code, contributed by Padmapani Seneviratne, minimum distance computed by Markus Grassl:
[96,49,22]4
2 derived codes
2020-08-21
code [109,48,28]4
via Construction X from constacyclic codes
4 derived codes
2020-08-12
constacyclic code [105,45,28]4
6 derived codes
2020-08-09
constacyclic code [105,60,20]4
25 derived codes
2020-08-05
quasicyclic code from a skew-cyclic code, contributed by Padmapani Seneviratne:
[72,36,29]4
6 derived codes
2020-08-03
codes [98,42,27]4, [101,42,28]4 using Construction X
2 derived codes
2020-08-03
quasicyclic code [96,41,27]4
code [98,41,28]4 using Construction X
7 derived codes
2020-07-29
code [97,40,28]4 using Construction X
code [97,45,25]4 using Construction X
code [99,46,25]4 using Construction XX
2020-07-28
quasicyclic code [96,44,25]4
code [98,40,28]4 using Construction X
2 derived codes
2020-07-27
quasicyclic codes from skew-cyclic codes, contributed by Padmapani Seneviratne:
[96,39,28]4, [96,40,27]4
2 derived codes
2020-07-24
quasicyclic code [96,43,26]4
code [98,44,26]4 using Construction X
14 derived codes in total
2020-07-18
cyclic code [113,42,36]4
63 derived codes
2020-07-17
quasicyclic codes from skew-cyclic codes, contributed by Padmapani Seneviratne:
[52,28,13]4, [56,22,20]4, [56,23,19]4, [56,29,15]4, [72,34,20]4, [72,35,19]4, [72,37,18]4, [72,38,17]4, [64,29,19]4
17 derived codes

GF(5)

2021-08-13
applying Construction X to cyclic and quasicyclic codes, contributed by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey:
[65,51,8]5, [81,18,40]5
2021-08-12
quasicyclic codes and codes applying Construction X to quasicyclic codes, contributed by Eric Chen:
[39,10,21]5, [68,11,40]5, [73,9,47]5, [75,11,45]5, [93,9,62]5,
2 derived codes

GF(7)

2023-02-22
code [59,17,29]7 via Construction X using cyclic codes [57,17,27]7 and [57,16,29]7,
1 derived code
2021-08-26
code [81,15,47]7 via puncturing of constacyclic code [93,15,58]7
2021-08-19
constacyclic code [93,15,58]7 by Dev Akre, Nuh Aydin, Matthew J. Harrington, Saurav Pandey arXiv:2108.08619,
21 derived codes

GF(8)

GF(9)

Quantum Codes

qubit codes

2024-05-06
codes [[109,37,16]]2, [[111,3,25]]2, [[114,0,26]]2, and [[183,123,11]]2
416 derived codes (improved and missing codes)
Reza Dastbasteh, Farzad Padashnick, Pedro M. Crespo, Markus Grassl, and Javad Sharafi,
"Equivalence of constacyclic codes with shift constants of different orders",
preprint arXiv:2403.04600 [cs.IT], march 2024.
2024-05-06
codes [[22,2,7]]2, [[37,17,6]]2, [[45,10,9]]2, [[51,8,11]]2, [[52,16,10]]2, and [[52,24,8]]2
14 derived codes
Reza Dastbasteh and Khalil Shivji.
"Polynomial Representation of Additive Cyclic Codes and New Quantum Codes."
preprint arXiv:2301.00753 [cs.IT], January 2023.
2024-04-24
cyclic code [[60,38,6]]2
1 derived code
Kanat Abdukhalikov, Tushar Bag, and Daniel Panario
"One-generator quasi-cyclic codes and their dual codes."
Discrete Mathematics, vol. 346, no. 6., 113369, June 2023.
DOI 10.1016/j.disc.2023.113369
cyclic code [[63,42,6]]2
1 derived code
Yiting Liu, Chaofeng Guan, Chao Du and Zhi Ma.
"Lower Bounds for Quasi-Cyclic Codes and New Binary Quantum Codes."
Symmetry, vol. 15, no. 3, article no. 643, 2023
DOI 10.3390/sym15030643
[[64,53,4]]2 and [[241,193,8]]2
from a Quantum Twisted Code and a cyclic linear code
35 derived codes and 44 missing codes
Reza, Dastbasteh,
"New quantum codes, minimum distance bounds, and equivalence of codes",
PhD thesis, Simon Fraser University, 2023
[[68,40,7,19]]2 and [[70,48,5]]2
using extensions of cyclic linear codes 5 derived codes
J. Wang, R. Li, J. Lv and H. Song,
" New Method of Constructing Binary Quantum Codes From Arbitrary Quaternary Linear Codes,"
IEEE Communications Letters, vol. 24, no. 3, pp. 472-476, March 2020,
DOI 10.1109/LCOMM.2019.2961353
[[102,70,7]]2 from a quasi-cyclic linear codes 2 derived codes
J. Lv, R. Li and J. & Wang, J,
"Constructions of quasi-twisted quantum codes."
Quantum Information Processiing vol. 19, article no. 274, 2020.
DOI 10.1007/s11128-020-02742-1
2023-01-03
[[77,0,19]]2 and [[90,0,22]]2 by Padmapani Seneviratne et al.
2 derived codes
Padmapani Seneviratne, Hannah Cuff, Alexandra Koletsos, Kerry Seekamp, Adrian Thnanopavarn
"New Qubit Codes from Multidimensional Circulant Graphs",
arXiv:2309.01798.07137 [cs.IT]
2023-01-03
[[40,6,10]]2 found by Padmapani Seneviratne from a skew-cyclic (quasi-cyclic) GF(4)-linear code
12 derived codes
2022-11-27
[[79,11,15]]2 from random GF(4)-linear code
3 derived codes
2022-11-10
[[54,32,6]]2 found by Dastbasteh & Lisonek using quantum Construction X on a yclic code arXiv 2211.00897
1 derived code
2022-11-10
[[114,72,9]]2 found by Dastbasteh & Lisonek using quantum Construction X on a constacyclic code arXiv 2211.00897
[[113,73,9]]2 applying quantum Construction X to a supercode of a constayclic code
35 derived codes
2022-08-02
additive cyclic codes [[45,16,8]]2, [[47,23,7]]2, [[51,26,7]]2, [[55,20,9]]2, [[55,25,8]]2, [[63,31,8]]2, [[91,60,7]]2, [[93,63,7]]2, and [[105,74,7]]2 by Chaofeng Guan, Ruihu Li, Liangdong Lu, and Yu Yao,
26 derived codes
Chaofeng Guan, Ruihu Li, Liangdong Lu, and Yu Yao,
"New Binary Quantum Codes Constructed from Quasi-Cyclic Codes",
arXiv:2112.07137 [cs.IT]

qutrit codes

2024-06-10
cylic codes [[13,6,4]]3, [[16,6,5]]3, and [[23,12,5]]3 found by Tushar Bag and Omar Fawzi

ququad codes

2024-06-07
non-existence of codes [[7,1,4]]4 and [[8,0,5]]4
Simeon Ball, Edgar Moreno, and Robin Simoens,
"Stabiliser codes over fields of even order",
arXiv:2401.06618 [math.CO]