The Blade Of The East is a unique variant of the Bumper Sword that can be found on Legate Lanius, who you fight at the end of the main quest of the NCR, Mr. House, and Yes Man main story quest routes.

Quick tips and notes about the Blade Of The East:

• Effectively unobtainable. Despite it being technically obtainable, it can only be found on one of the last enemies you’ll ever encounter in the game. Without mods (which are only available on PC) that allow you to play after the game’s ending, you won’t be able to use this weapon throughout your regular playthrough.
• Has an obtainable counterpart. The Lonesome Road DLC adds a more permanently obtainable and arguably more powerful counterpart called the Blade Of The West. More info on that sword here. 
• You must kill Legate Lanius to get the weapon. Legate Lanius is one of the most powerful enemies in the entire game. He’s fast, his sword deals 100 damage or more per swing, has nearly 1,000 HP, is immune to poison, and is almost immune to fire. 

Acquisition

To get this weapon, you’ll have to get to the end of the main questline of either the NCR, Mr. House, or Yes Man. 

Near the end of the final battle, you’ll make it to a location called “Legate’s Camp”. 

Follow the quest marker down into the main camp. You’ll eventually make it to a flight of stairs leading up a hill. Walk up these stairs.

About ¾ of the way up, you’ll see the Legate. If you want to get this weapon, don’t bother talking to him, just attack him and kill him as fast as possible. Use the distance to your advantage.

Once he’s dead, you can loot the sword from his corpse.

Comparing The Blade Of The East To The Blade Of The West.

While the sword is a unique variant of the Bumper Sword, it beats that weapon in pretty much every single way. A far more interesting comparison is between it and the Blade Of The West from the Lonesome Road DLC:

• The Blade Of The East deals 5 more damage (65 damage vs 60 damage).
• The Blade Of The East has a special poison effect that deals 2 damage per second for 10 seconds.
• The Blade Of The East is far more durable (3995 attacks before breaking vs 745 attacks before breaking).

Here’s where the benefits of the Blade Of The East end.

• The Blade Of The West attacks faster (2.13 attacks/second vs 1.58 attacks/second), which also results in more damage per second (128 damage per second vs 103 damage per second).
• The Blade Of The West has a higher critical hit chance multiplier (1.5x vs 1x).
• The Blade Of The West costs fewer AP to attack with in VATS (29 AP to attack vs 35 AP to attack).

Gameplay Tips

• If you are playing on PC, and want to try the weapon out, you can use the following console command to give yourself the sword: “player.additem 00143FBA”.
• Due to the stats being overall inferior when compared to the Blade Of The West, there’s no real reason to acquire this version, even if you could.
• It’s possible for Lanius to equip a pistol when he can’t reach the player. This will make getting the sword impossible.