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# 1.How to make it short

1. How to make it short

Generally speaking, making something simple or short is considered as “compressing”. Thus, first of all, “Data compression” technology is considered to make latitude/longitude shorter. However, data which is target of compression is only a set of latitude and longitude- only two numeric values. So it is very difficult to apply usual data compression method, such as Hoffman-compression, ZIP, etc.

Assume that the Earth’s meridian is 40,000,000 meters, and the equator is also 40,000,000 meter. To identify location with 1 meter by 1 meter precision,

20,000,000 meter (a half of meridian) multiplied by 40,000,000 meter = 8 * 10^14 combinations

are needed. This is equal to:

log 2 (8 * 10^14) = 49.507 bit of information amount

Now, there are two approaches to make it short.

The first approach is reducing the amount of information, by limiting area, or reducing precision.

For example, “MapCode” reduce the amount of information needed, by limiting a cover area for only land area in Japan, and decrease precision to 30meter. Then MapCode™ can locate anywhere in Japan with only 10 digit of numbers. This is suitable foe car navigation purpose.

Another approach is called “Length compression”. To express 49.507 bit of information amount, 50 digits needed in binary expression. 15 digits needed as decimal. In Theory, if you use notation system that base radix is higher than 10, it should be shorter than latitude and longitude, because they are in decimal.

Base of Radix Digits length needed Example of letter used Example

2 (Binary) 0,1 01101010011001

00101100111001

00101011100100

10100101

10(decimal) 15 0-9 35.12345, 135.12345

16(hexadecimal) 13 0-9 and A-F 3745CD874E6A1

26 11 A-Z ESQANYGFRG

36 10 0-9 and A-Z HESB6D3F5L

60 9 0-9, A-Z, a-x gyFuJ8y1c

10000 4 Chinese Kanji

Figure 1: Base radix and code length needed

Decimal based GEOCODE, including latitude/longitude coordinate, needs 15 numbers to express about 1 by 1 meter precision. 15 numbers is almost the same length of credit card number (16 numbers), and it is hard to handle for human without a tool. Hexadecimal based GEOCDE realize 13 digits, but it usually become like "28a6f6b021cf3", and it is still difficult to handle. If you use 10000 different characters like Chinese Character Set, only 4 letters can express location. However, it must be hard to recognize or remember 10000 different Kanji Characters.

As table above and following chart shows, increasing radix base number does not have linear effect for its length. If radix base is more than 36 or 60, the effectiveness of rising radix base number won’t decrease code length effectively.

Some GEOCODEs, such as LocaPoint, LP-Address, and Maidenhead Locator System, used complex-radix notation. In short, they use different radix-base for different digits in its format. However, they are still following the same rule.

Chart 1: Radix base and minimum length for 800000000000000 values.