On the classification of quaternary Hermitian LCD codes

This page lists generator matrices of quaternary Hermitian LCD [n,k] codes given in the following paper:
Makoto Araya and Masaaki Harada, On the classification of quaternary Hermitian LCD codes, preprint.

Table 2: Classification for lengths up to 11

n	k	N	N₁	N₂	N₃	N₄	N₅	N₆	N₇	N₈
4	2	4	2	2
5	2	6	2	3	1
	3	6	4	2
6	2	11	3	4	3	1
	3	13	6	5	2
	4	11	6	5
7	2	16	3	5	4	3	1
	3	36	11	13	11	1
	4	36	13	20	3
	5	16	11	5
8	2	25	4	6	6	5	3	1
	3	80	16	22	31	10	1
	4	176	36	84	49	7
	5	80	36	40	4
	6	25	16	9
9	2	34	4	7	7	7	5	4
	3	227	25	42	76	55	28	1
	4	993	80	305	372	235	1
	5	993	176	496	311	10
	6	227	80	141	6
	7	34	25	9
10	2	51	5	8	9	9	9	9	2
	3	545	34	63	144	140	150	14
	4	7454	227	1081	2101	3490	554	1
	5	19043	993	4996	9455	3598	1
	6	7454	993	4380	2064	17
	7	545	227	312	6
	8	51	34	17
11	2	68	5	9	10	11	11	15	5	2
	3	1492	51	104	259	325	543	197	13
	4	56310	545	3381	8521	25215	17681	967
	5	525396	7454	52492	170767	271667	23015	1
	6	525396	19043	151868	280517	73967	1
	7	56310	7454	35669	13185	2
	8	1492	545	941	6
	9	68	51	17

Table 3: Classification for length 12(k≠6)

n	k	N	N₁	N₂	N₃	N₄	N₅	N₆	N₇	N₈	N₉
12	2	95	6	10	12	13	15	21	11	6	1
	3	3654	68	146	414	581	1298	868	277	2
	4	439007	1492	10369	31140	125753	196104	74001	148
	5	14405773(12-5.magma.gz(207.4MB))	56310	480063	2086894	7114373	4653183	14950
	7	14405773(12-7.magma.gz(238.6MB))	525396	4520230	8275240	1084907
	8	439007	56310	303556	79139	2
	9	3654	1492	2156	6
	10	95	68	27

Table 4: |C(12,6,d)|(d=1,2,3,4,5)

d	1	2	3	4	5
\|C(12,6,d)\|	525396	5343280	18671418	27364559	503800

Table 5: Classification for dimension 2 (n=13,14,...,50)

n	\|C(n,2)\|	\|C(n,2,*,1)\|	\|C(n,2,1,>= 2)\|	\|C(n,2,>= 2,>= 2)\|
13	122	95	0	27
14	166	122	1	43
15	210	166	0	44
16	275	210	1	64
17	340	275	0	65
18	436	340	1	95
19	532	436	0	96
20	666	532	1	133
21	800	666	0	134
22	986	800	1	185
23	1172	986	0	186
24	1420	1172	1	247
25	1668	1420	0	248
26	1997	1668	1	328
27	2326	1997	0	329
28	2750	2326	1	423
29	3174	2750	0	424
30	3717	3174	1	542
31	4260	3717	0	543
32	4941	4260	1	680
33	5622	4941	0	681
34	6471	5622	1	848
35	7320	6471	0	849
36	8361	7320	1	1040
37	9402	8361	0	1041
38	10672	9402	1	1269
39	11942	10672	0	1270
40	13471	11942	1	1528
41	15000	13471	0	1529
42	16832	15000	1	1831
43	18664	16832	0	1832
44	20836	18664	1	2171
45	23008	20836	0	2172
46	25572	23008	1	2563
47	28136	25572	0	2564
48	31136	28136	1	2999
49	34136	31136	0	3000
50	37633	34136	1	3496

Table 6: Classification for dimension 2 (n=51,52,...,70)

n	\|C(n,2)\|	\|C(n,2,*,1)\|	\|C(n,2,1,>= 2)\|	\|C(n,2,>= 2,>= 2)\|
51	41130	37633	0	3497
52	45176	41130	1	4045
53	49222	45176	0	4046
54	53887	49222	1	4664
55	58552	53887	0	4665
56	63897	58552	1	5344
57	69242	63897	0	5345
58	75347	69242	1	6104
59	81452	75347	0	6105
60	88387	81452	1	6934
61	95322	88387	0	6935
62	103178	95322	1	7855
63	111034	103178	0	7856
64	119891	111034	1	8856
65	128748	119891	0	8857
66	138708	128748	1	9959
67	148668	138708	0	9960
68	159822	148668	1	11153
69	170976	159822	0	11154
70	183438	170976	1	12461

Table7: Classification for dimension 3

n	\|C(n,3)\|	\|C(n,3,*,1)\|	\|C(n,3,1,>=2)\|	\|C(n,3,>=2,>=2)\|
13	9390	3654	27	5709
14	22198	9390	27	12781
15	53176	22198	44	30934
16	119549	53176	44	66329
17	267687	119549	65	148073
18	571248	267687	65	303496
19	1205587	571248	96	634243
20	2449822	1205587	96	1244139

Table 8: |C(5s+t,2,d4H(5s+t,2)-2,>=2)| (t=0,1,2,4)

t \ s	1	2	3	4	5	6	7	8	9	10	11
0	0	4	7	15	17	22	23	25	26	27	27
1	1	6	13	20	25	29	31	33	34	35
2	1	6	8	13	14	16	17	18	18
4	2	9	18	26	33	38	42	44	46	47	48

Table 9: |C(5s+t,2,d4H(5s+t,2)-3,>= 2)| (t=0,1,2,3,4)

t \ s	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
0		2	10	22	36	49	60	68	75	80	84	86	88	89	90
1	1	2	11	15	28	32	40	42	47	48	50	51	52	52
2	1	6	16	28	39	47	54	59	63	65	67	68	69
3	2	4	14	18	26	28	33	34	36	37	38	38
4	1	8	12	27	32	45	49	57	59	64	65	67	68	69	69

Table 10: |C(n,k,d)| (n=13,14,15)

(n,k)	(13,2)	(13,3)	(13,4)	(14,2)	(14,3)	(14,4)	(15,2)	(15,3)	(15,4)
d=1	6	95	3654	7	122	9390	7	166	22198
d=2	11	220	29160	12	295	79947	13	419	205367
d=3	13	651	98177	15	952	293566	16	1380	806069
d=4	15	1030	486075	17	1591	1644965	19	2477	4971898
d=5	17	2685	1171975	21	4736	5132359	23	7912	18230789
d=6	27	2637	1294025	33	5686	10425403	39	11075	53126171
d=7	15	1914	127290	23	6787	4835373	27	17504	56708122
d=8	13	156	19	22	1871	183997	32	9309	15426964
d=9	4	2		11	158		18	2906	50831
d=10	1			5			14	28
d=11							2
(n,k)	(13,11)	(13,10)	(13,9)	(14,12)	(14,11)	(14,10)	(15,13)	(15,12)	(15,11)
d=1	95	3654	439007	122	9390	3210375	166	22198	22605000
d=2	27	5732	2332236	44	12805	17147192	44	30976	116330805(part1, part2, part3, part4, part5, part6)
d=3		4	439130		3	2247433		2	10612604
d=4			2
Total	122	9390	3210375	166	22198	22605000	210	53176	149548409

On the minimum weights of quaternary Hermitian LCD codes

This page lists generator matrices of quaternary (unrestricted) [n,k] codes given in the following paper:
Makoto Araya and Masaaki Harada, On the minimum weights of quaternary Hermitian LCD codes, Cryptography and Communications, Volume 16, 2024, Pages 1539–1558.

Table 1: Numbers Nw(n, k, d) and N(n, k, d)

(n,k,d)	Generator matrix
(14,5, 8)	9
(15,4,10)	1
(15,6, 8)	3
(16,4,11)	1
(17,4,12)	1
(18,4,12)	26
(22,4,15)	24
(23,4,16)	4
(23,5,15)	3
(24,5,16)	1
(27,4,19)	4
(28,4,20)	1
(30,4,21)	6

Table 7: Numbers of inequivalent quaternary (unrestricted) [n,k] codes

n\k	1	2	3	4	5	6
1	1
2	2
3	3
4	4	7
5	5	13
6	6	22	37
7	7	34	92
8	8	51	223	415
9	9	73	541	2199
10	10	103	1313	14293	38676
11	11	140	3194	103730	962654
12	12	188	7762	772652	26087225

Appendix: orders of the automorphism group of [n,k] codes in Table 7

n\k	1	2	3	4	5	6
1	1
2	2
3	3
4	4	7
5	5	13
6	6	22	37
7	7	34	92
8	8	51	223	415
9	9	73	541	2199
10	10	103	1313	14293	38676
11	11	140	3194	103730	962654
12	12	188	7762	772652	26087225

On the classification of certain ternary codes of length 12

This page lists generator matrices of some ternary codes given in the following paper:
Makoto Araya and Masaaki Harada, On the classification of certain ternary codes of length 12, Hiroshima Mathematical Journal, Volume 45, Number 1, 2016, Pages 87-96.

Theorem 1

Proposition 5

On Some Optimal Linear Codes over F₅

This page lists generator matrices of some optimal codes over F₅ given in the following paper:
Makoto Araya and Masaaki Harada, On Some Optimal Linear Codes over F₅, Discrete Mathematics, Volume 313, Issue 24, 28 December 2013, Pages 2872--2874.

On the classification of quaternary Hermitian LCD codes

On the minimum weights of quaternary Hermitian LCD codes

On the classification of certain ternary codes of length 12

Theorem 1

Proposition 5

On Some Optimal Linear Codes over F5

Table 1:

Table 2:

Table 3:

On Some Optimal Linear Codes over F₅