More than 223 Hadamard matrices (HdM) of orders 4N up to the order N=2000 will be available on this page. The coefficients 1 and -1 of matrices of large sizes will be denoted by + and -, respectively. Such matrices can be viewed and downloaded. All matrices are divided by three classes and presented here in form of tables. Such a three-color table of Hadamard matrices will be posted soon. The equivalency of these matrices with the existent ones is not analyzed; our goal is to compose ourselves the whole table of matrices 4Nx4N. We started this work on the middle of October 2008 and knew no much about constructions of Hadamard matrices. Our methods are unique and codes are simple and will be published as soon as we finish this work.
Art and Merughan Grigoryans / November 30, 2008.

The first class which contain 155 matrices and corerspond to the case when 4N-1 are primes have been generated by a simple code developed and tested on October 25, 2008. The marices are of orders: 4, 8, 12, 20, 24, 32, 44, 48, 60, 68, 72, 80, 84, 104, 108, 128, 132, 140, 152, 164, 168, 180, 192, 200, 212, 224, 228, 240, 252, 264, 272, 284, 308, 312, 332, 348, 360, 368, 380, 384, 420, 432, 440, 444, 464, 468, 480, 488, 492, 500, 504, 524, 548, 564, 572, 588, 600, 608, 620, 632, 644, 648, 660, 684, 692, 720, 728, 740, 744, 752, 788, 812, 824, 828, 840, 860, 864, 884, 888, 908, 912, 920, 948, 968, 972, 984, 992, 1020, 1032, 1040, 1052, 1064, 1088, 1092, 1104, 1124, 1152, 1164, 1172, 1188, 1224, 1232, 1260, 1280, 1284, 1292, 1304, 1308, 1320, 1328, 1368, 1400, 1424, 1428, 1440, 1448, 1452, 1460, 1472, 1484, 1488, 1500, 1512, 1524, 1532, 1544, 1560, 1568, 1572, 1580, 1584, 1608, 1620, 1628, 1664, 1668, 1700, 1724, 1748, 1760, 1784, 1788, 1812, 1824, 1832, 1848, 1868, 1872, 1880, 1908, 1932, 1952, 1980, 1988, 2000.
The matrices which are already in this class are highlighted by red color. We name each matrix NxN of this class as had.N.m1.grigoryan, for instance, had.12.m1.grigoryan for the matrix 12x12.
[All matrices of this class are now available / December 2, 2008].

4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
84	88	92	96	100	104	108	112	116	120	124	128	132	136	140	144	148	152	156	160
164	168	172	176	180	184	188	192	196	200	204	208	212	216	220	224	228	232	236	240
244	248	252	256	260	264	268	272	276	280	284	288	292	296	300	304	308	312	316	320
324	328	332	336	340	344	348	352	356	360	364	368	372	376	380	384	388	392	396	400
404	408	412	416	420	424	428	432	436	440	444	448	452	456	460	464	468	472	476	480
484	488	492	496	500	504	508	512	516	520	524	528	532	536	540	544	548	552	556	560
564	568	572	576	580	584	588	592	596	600	604	608	612	616	620	624	628	632	636	640
644	648	652	656	660	664	668	672	676	680	684	688	692	696	700	704	708	712	716	720
724	728	732	736	740	744	748	752	756	760	764	768	772	776	780	784	788	792	796	800
804	808	812	816	820	824	828	832	836	840	844	848	852	856	860	864	868	872	876	880
884	888	892	896	900	904	908	912	916	920	924	928	932	936	940	944	948	952	956	960
964	968	972	976	980	984	988	992	996	1000	1004	1008	1012	1016	1020	1024	1028	1032	1036	1040
1044	1048	1052	1056	1060	1064	1068	1072	1076	1080	1084	1088	1092	1096	1100	1104	1108	1112	1116	1120
1124	1128	1132	1136	1140	1144	1148	1152	1156	1160	1164	1168	1172	1176	1180	1184	1188	1192	1196	1200
1204	1208	1212	1216	1220	1224	1228	1232	1236	1240	1244	1248	1252	1256	1260	1264	1268	1272	1276	1280
1284	1288	1292	1296	1300	1304	1308	1312	1316	1320	1324	1328	1332	1336	1340	1344	1348	1352	1356	1360
1364	1368	1372	1376	1380	1384	1388	1392	1396	1400	1404	1408	1412	1416	1420	1424	1428	1432	1436	1440
1444	1448	1452	1456	1460	1464	1468	1472	1476	1480	1484	1488	1492	1496	1500	1504	1508	1512	1516	1520
1524	1528	1532	1536	1540	1544	1548	1552	1556	1560	1564	1568	1572	1576	1580	1584	1588	1592	1596	1600
1604	1608	1612	1616	1620	1624	1628	1632	1636	1640	1644	1648	1652	1656	1660	1664	1668	1672	1676	1680
1684	1688	1692	1696	1700	1704	1708	1712	1716	1720	1724	1728	1732	1736	1740	1744	1748	1752	1756	1760
1764	1768	1772	1776	1780	1784	1788	1792	1796	1800	1804	1808	1812	1816	1820	1824	1828	1832	1836	1840
1844	1848	1852	1856	1860	1864	1868	1872	1876	1880	1884	1888	1892	1896	1900	1904	1908	1912	1916	1920
1924	1928	1932	1936	1940	1944	1948	1952	1956	1960	1964	1968	1972	1976	1980	1984	1988	1992	1996	2000

The second class which contain 87(88) matrices was generated by a code developed and tested on November 26, 2008. The marices are of orders: 8*, 16, 24*, 40, 48*, 64, 88, 96, 120, 136, 144, 160, 168*, 208, 216, 256, 264*, 280, 304, 328, 336, 360*, 384*, 400, 424, 448, 456, 480*, 504*, 528, 544, 568, 616, 624, 664, 696, 720, 736, 760, 768, 840*, 864*, 880, 888*, 928, 936, 960, 976, 984, 1000, 1008, 1048, 1096, 1128, 1144, 1176, 1200, 1216, 1240, 1264, 1288, 1296, 1320*, 1368*, 1384, 1440*, 1456, 1480, 1488*, 1504, 1576, 1624, 1648, 1656, 1680, 1720, 1728, 1768, 1776, 1816, 1824*, 1840, 1896, 1936, 1944, 1968, 1984, 2040.
We name each matrix NxN of this class as had.N.m2.grigoryan. The matrices which are already in this class are highlighted by blue color.
[All matrices of the 2nd class are now available / December 9, 2008].

4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
84	88	92	96	100	104	108	112	116	120	124	128	132	136	140	144	148	152	156	160
164	168	172	176	180	184	188	192	196	200	204	208	212	216	220	224	228	232	236	240
244	248	252	256	260	264	268	272	276	280	284	288	292	296	300	304	308	312	316	320
324	328	332	336	340	344	348	352	356	360	364	368	372	376	380	384	388	392	396	400
404	408	412	416	420	424	428	432	436	440	444	448	452	456	460	464	468	472	476	480
484	488	492	496	500	504	508	512	516	520	524	528	532	536	540	544	548	552	556	560
564	568	572	576	580	584	588	592	596	600	604	608	612	616	620	624	628	632	636	640
644	648	652	656	660	664	668	672	676	680	684	688	692	696	700	704	708	712	716	720
724	728	732	736	740	744	748	752	756	760	764	768	772	776	780	784	788	792	796	800
804	808	812	816	820	824	828	832	836	840	844	848	852	856	860	864	868	872	876	880
884	888	892	896	900	904	908	912	916	920	924	928	932	936	940	944	948	952	956	960
964	968	972	976	980	984	988	992	996	1000	1004	1008	1012	1016	1020	1024	1028	1032	1036	1040
1044	1048	1052	1056	1060	1064	1068	1072	1076	1080	1084	1088	1092	1096	1100	1104	1108	1112	1116	1120
1124	1128	1132	1136	1140	1144	1148	1152	1156	1160	1164	1168	1172	1176	1180	1184	1188	1192	1196	1200
1204	1208	1212	1216	1220	1224	1228	1232	1236	1240	1244	1248	1252	1256	1260	1264	1268	1272	1276	1280
1284	1288	1292	1296	1300	1304	1308	1312	1316	1320	1324	1328	1332	1336	1340	1344	1348	1352	1356	1360
1364	1368	1372	1376	1380	1384	1388	1392	1396	1400	1404	1408	1412	1416	1420	1424	1428	1432	1436	1440
1444	1448	1452	1456	1460	1464	1468	1472	1476	1480	1484	1488	1492	1496	1500	1504	1508	1512	1516	1520
1524	1528	1532	1536	1540	1544	1548	1552	1556	1560	1564	1568	1572	1576	1580	1584	1588	1592	1596	1600
1604	1608	1612	1616	1620	1624	1628	1632	1636	1640	1644	1648	1652	1656	1660	1664	1668	1672	1676	1680
1684	1688	1692	1696	1700	1704	1708	1712	1716	1720	1724	1728	1732	1736	1740	1744	1748	1752	1756	1760
1764	1768	1772	1776	1780	1784	1788	1792	1796	1800	1804	1808	1812	1816	1820	1824	1828	1832	1836	1840
1844	1848	1852	1856	1860	1864	1868	1872	1876	1880	1884	1888	1892	1896	1900	1904	1908	1912	1916	1920
1924	1928	1932	1936	1940	1944	1948	1952	1956	1960	1964	1968	1972	1976	1980	1984	1988	1992	1996	2000

The third class of Hadamard matrices is generated by a new code [November 30, 2008]. The marices are of orders: 12,20,28,36,44, ... . We name each matrix NxN of this class as had.N.m5.grigoryan.

4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80
84	88	92	96	100	104	108	112	116	120	124	128	132	136	140	144	148	152	156	160
164	168	172	176	180	184	188	192	196	200	204	208	212	216	220	224	228	232	236	240
244	248	252	256	260	264	268	272	276	280	284	288	292	296	300	304	308	312	316	320
324	328	332	336	340	344	348	352	356	360	364	368	372	376	380	384	388	392	396	400
404	408	412	416	420	424	428	432	436	440	444	448	452	456	460	464	468	472	476	480
484	488	492	496	500	504	508	512	516	520	524	528	532	536	540	544	548	552	556	560
564	568	572	576	580	584	588	592	596	600	604	608	612	616	620	624	628	632	636	640
644	648	652	656	660	664	668	672	676	680	684	688	692	696	700	704	708	712	716	720
724	728	732	736	740	744	748	752	756	760	764	768	772	776	780	784	788	792	796	800
804	808	812	816	820	824	828	832	836	840	844	848	852	856	860	864	868	872	876	880
884	888	892	896	900	904	908	912	916	920	924	928	932	936	940	944	948	952	956	960
964	968	972	976	980	984	988	992	996	1000	1004	1008	1012	1016	1020	1024	1028	1032	1036	1040
1044	1048	1052	1056	1060	1064	1068	1072	1076	1080	1084	1088	1092	1096	1100	1104	1108	1112	1116	1120
1124	1128	1132	1136	1140	1144	1148	1152	1156	1160	1164	1168	1172	1176	1180	1184	1188	1192	1196	1200
1204	1208	1212	1216	1220	1224	1228	1232	1236	1240	1244	1248	1252	1256	1260	1264	1268	1272	1276	1280
1284	1288	1292	1296	1300	1304	1308	1312	1316	1320	1324	1328	1332	1336	1340	1344	1348	1352	1356	1360
1364	1368	1372	1376	1380	1384	1388	1392	1396	1400	1404	1408	1412	1416	1420	1424	1428	1432	1436	1440
1444	1448	1452	1456	1460	1464	1468	1472	1476	1480	1484	1488	1492	1496	1500	1504	1508	1512	1516	1520
1524	1528	1532	1536	1540	1544	1548	1552	1556	1560	1564	1568	1572	1576	1580	1584	1588	1592	1596	1600
1604	1608	1612	1616	1620	1624	1628	1632	1636	1640	1644	1648	1652	1656	1660	1664	1668	1672	1676	1680
1684	1688	1692	1696	1700	1704	1708	1712	1716	1720	1724	1728	1732	1736	1740	1744	1748	1752	1756	1760
1764	1768	1772	1776	1780	1784	1788	1792	1796	1800	1804	1808	1812	1816	1820	1824	1828	1832	1836	1840
1844	1848	1852	1856	1860	1864	1868	1872	1876	1880	1884	1888	1892	1896	1900	1904	1908	1912	1916	1920
1924	1928	1932	1936	1940	1944	1948	1952	1956	1960	1964	1968	1972	1976	1980	1984	1988	1992	1996	2000

Merughan, we need to add here one more table for your uniqie method of generating the Hadamard matrices of orders N=4n. The first 12 matrices obtained by using this method are given below. We name such matrices NxN as had.N.mgrigoryan, respectively.

4	8	12	16	20	24	28	32	36	40	44	48	52	56	60	64	68	72	76	80	84	88	92	96	100

December 25, 2008